When he asks her to marry him, it's spur-of-the-moment. He doesn't plan it out, regale her with a flowery speech, or even have a ring on his person. But it's perfect and anything more would be fake (and when you're surrounded by lies and deception 98% of your waking hours, you crave truth like a strung-out addict craves coke).
They're fielding enemy fire from rogue Nicaraguans in the middle of a forest so dense everything but them is a canvas of green and their only savior is heat-seeking technology. He's losing arrows left and right, switching to a rifle every third shot to preserve his quiver. Natasha's popping off rounds with her usual flourish, twirling like an acrobat. She's mesmerizing and lethal and he could never imagine himself with anyone less. Abruptly, she unsheathes a stiletto knife from her back and races to duck under nearby brush for further cover. He recognizes the signal the instant her hand brushes the blade and he slides to a halt under the foliage a second after.
It's in that moment, in the shadows, where they've made their lives (her from the throes of Russia and slews of potentials to emerge victorious; him from a broken childhood to circus tents to mercenaries; even as the good guys, the shadows are their home and they only venture into the light as others – false identities, new aliases, fabricated covers), that he realizes they're going to spend the rest of their lives together. They won't stop because they're made for this, forged from rusty blood and searing wounds, sculpted from pain and loss and tragedy, so wholly changed they could never do anything else.
They could never be with anyone else.
So in that moment, as the bullets are still flying and they're knee-deep in squishy soil, as a worm slinks across his thigh (exposed flesh thanks to catching the business end of a tree branch) and a beetle scurries past Natasha, as they're huddled together like the last survivors in uninhabitable terrain, he proposes. It comes out as a jumble of words and in his hurry he's tumbling over languages so every other word comes out a different dialect (Latin to Bulgarian to Russian to Vietnamese to accented Hungarian to Portuguese to Armenian and back again); Natasha sure as hell can keep up, but it's nonetheless a bit of an oddity, even against their weird experiences.
He receives a look of confused understanding in return and what may be an affirmative nod but doesn't get a verbalized answer until they finally eliminate the last two terrorists. He isn't distracted from the task at hand as he snipes one of their remaining attackers; he instinctively knows her answer because, despite her gruesome upbringing, as much as she gripes about feelings and love as nothing more than fantasies, he knows it's different for him. Their relationship may be one-in-the-same as their careers, kept in the darkness, hidden in the shadows, but it's real. In a fit of adrenaline-induced clarity, he suddenly realizes what triggered his motivation that day: it's the first op they've had in eighteen months that wasn't laced in deceit and subterfuge; it was concrete, like their connection. Though, unlike the mission, their passion and commitment to one another is something no one else will ever fully grasp no matter how many psych degrees or Black Widow/Hawkeye personnel reports they have in their files.
They're not wearing comms (at least, not anymore, they lost the little devices on the jungle floor within their first ten minutes and any signal to the outside world four before that) so there is absolutely no chance of being overheard as their only possible witnesses lie scattered across the forest floor, vacant carcasses awaiting extraction. Dead men tell no tales and all that, so their secret will remain safe (since there's no point in establishing a secret if somebody can find out about it).
Natasha covertly signs a 'yes' to Clint, because even in the abandoned environment they're currently stationed in, old habits die hard. Clint smiles a lopsided grin which is returned by Natasha's small smile, and they're both such genuine expressions of elation and exuberance over the coy or sarcastic countenances they usually carry. They kiss, all hot and eager and grateful, like that very first time three years after her recruitment, but this time it's even better because their love amplifies the pleasure tenfold.
They fly back home after the SHIELD team deals with the bodies and continue on with their lives like nothing has happened. There's still that ever-present sexual tension floating in the air and the other agents will still gossip about them around the water cooler, but they let them. Their relationship is stronger than ever and they're still the most sought-after people on SHIELD's payroll (unfailingly fatal as individuals; unstoppably powerful as a team).
When he asks her to marry him, it's four years before they're Avengers.
Clint never buys her a ring and Natasha never asks him for one since jewelry is impermanent and easily destroyed in their line of work and she'd probably lose it anyway with their frequent location shifts (not to mention it would be undyingly irritable to constantly stash whenever she left her bedroom in hopes of maintaining their secret). Their version of engagement is akin to every other aspect of their relationship: unique and perfect for them, strange and unusual for anybody else.
They never get 'legally' married, but their lives haven't been exactly legal to begin with. In twenty-three countries they're declared dead, then another four for Tasha and another three for Clint. Even in the countries where their identities still live, there's arrest warrants or red flags next to one (or in eighteen cases, both) of their names. Plus marriage equals marriage license which leads to a paper trail and suddenly they're all over the radar for all sorts of notorious criminals and burned enemies and ex-employers to find them. There's a reason assassins keep a low profile and a marriage certificate is worse than a glowing neon sign or a spot on Interpol's Most Wanted list. A ratified marriage signals their ties to one another and then they're not only wanted for their own sins and actions but for those of the other. It's one giant liability that they both find wholly unnecessary.
Also, marriage tends to be precluded by a wedding and a wedding tends to require guests (yes, they could always go before a judge, but they tend to only get close to authority figures of that caliber when they're either seducing or killing them) and guests necessitate actually informing people of the existence of their relationship. They've seen enough TV and read enough tabloids between the two of them to know that recent weddings normally take extensive planning and energy that neither of them cares to sacrifice to what is little more than fancy bureaucracy. They have no time or desire for floral arrangements, caterers, or venues when they have assassinations, reconnaissance, and undercover operations to execute.
To them, paperwork is a symbol of sorts for death nowadays – whenever they kill or maim or ruin, they have to file it and account for it. They sit for hours on end cross-checking forms and assessing statements after missions. So they don't want their romance to be relegated to san-Serif font on bland cardstock paper for higher-ups to file away in a dusty cabinet and leave vulnerable for any schmuck to take.
Instead, they handle the marriage process their way. They get microscopic tattoos that, when their bodies lie on top of one another, directly connect. The tattoos join the plethora of scars on their bodies, but instead of tarnishing their flesh like the other marks, these new emblems enhance it. A teensy obsidian spider spins a dangerously thin crimson web on Clint's upper right thigh (strategically located to be hidden by any pair of boxers) and a tiny hawk head of the same obsidian perches on Natasha's left hip (also located to be hidden by any pair of panties). Both tattoos are little more than a centimeter across so even if they were stripped naked it would be hard to distinguish what the tattoo represented. They pay the tattoo artist cash because any idiot knows credit cards and checks leave electronic trails, and then tip the guy the monetary equivalent of $3500 American dollars to forget he ever inked a widow and a hawk. All of this happens on an island that doesn't legitimately exist.
They never truly officialize it. By society's standards it's still abstract since there's no document binding them together, but they know, they have the marks that are much harder to remove than a breakable ring. These tattoos identify them – they make it real – and for two assassins, that's all that matters.