So, this might be too specific, but do you know of any fics where Tony’s finally gotten the courage up to ask Steve on a date, but overhears/sees something that sweeps the rug out from under him and he loses his courage and backs off leaving Steve confused/hurt? But with happy endings where they actually get together in the end???

I don’t really know of anything quite that specific, but your ask lets me have the chance to do a First Date list, and so maybe you’ll find something you enjoy among these:

DON’T LET FEAR OF REJECTION KEEP YOU FROM LEAVING COMMENTS AND KUDOS!

First Date by @captainneverever:
Steve finally has a first date with Tony, but it doesn’t go as Steve expected.

Interruption by @captainneverever:
Steve has very important plans but Red Skull gets in the way.

Again and Again by @brandnewfashion:
The first time Tony kisses Steve is on their first official date.

Our Personal Fairytale by @pensversusswords:
In which there is a first date, a giant octopus, and Tony is scared of Ferris wheels.

Hit It Out’a The Park by snarkstark: Tony took a deep breath, trying to summon up all of his
courage. For fuck’s sake, he’d flew into a wormhole, fought countless
villains and made a suit of armour that made other engineer’s intentions
look like a Goddamn potato radio. He could ask Steve Rogers on a date.Or Tony is extra and Steve liked baseball.

always meet your heroes by navaan:
Iron Man is a beloved hero, but even he is amazed when Captain America appears back on the scene

Calamari a la Mode by @kagekanecavi:
There’s nothing that ruins a good date more than gigantic robotic tentacles.

This One’s Different Because It’s Us by allourheroes:
Despite the fact that they definitely have chemistry, Tony is certain Steve is fucking with him when he asks him out. He has to be, right?

One Night Is All I Need by PeggyElizabeth:
Steve couldn’t believe that he had landed a date with the Tony Stark. He also couldn’t believe that he was buried balls deep in the other man, but he wasn’t going to complain.

Wherever by @msermesth: Remember that time Steve got de-serumed and was super
bothered about it, but Tony was just excited Steve was letting him run
the tests? (Here’s a reminder)What if they had a date that night?

Anniversary by @lilmoongoddesss:
Tony invites Steve down into his lab for a black-tie, invitation only event.  Steve has no idea what hits him.

How Tony Stark Ruins Everything by aslipperysloth:
The story of how Tony Stark manages to ruin sex, dating, and friendship – in that order.

the meet cute by paxatonic:
Bucky and Steve sneak into a rich people’s party, where Steve gets roped into being Tony Stark’s date. What?

All the Difference in the World by @winterstar95:
It’s Tony’s luck that on his first date with Steve away from the
Academy, they end up abducted by AIM agents and it looks like their boss
just might reveal Tony’s big secret.

Flowers Are (Not) Mandatory by @izazov:
Tony is not freaking out over his upcoming date with Steve Rogers. Okay, maybe he is. But only a little.

Tulips and Violets by @laireshi:
It’s his first date with Steve, and Tony’s going to make sure it’s perfect.

Good Things Come To Those Who Wait (On the Bleachers) by SilverNoteXIII:
All Tony wanted to do was spend his lunch studying on the bleachers, he
didn’t expect Pepper to set him up on a study date with school football
player and long-time crush Steve Rogers. Steve may not have known about
Tony’s crush on him, but there are things about Steve even Tony doesn’t
know.

Night Out by @musicalluna:
Steve takes Tony out for their first date. The world is soft and shining and Tony thinks he’d like to stay this way forever.

Loving the Alien by love_in_the_stars:
A journey that starts with horrible first impressions and ends with a first date promise.

First Date(s) by ashinan:
Tony is a little slow on the uptake.

Small Hours Blues by @stark-spangled-lovers, morphia:
Steve and Tony finally get to their date, and immediately find
themselves in a curious predicament. Who’s to blame? Steve? Tony? Who
cares? Revelations are reached. Confessions are made. And at the end of
the night, the small hours darkness might’ve just been the best thing
that’d ever happened to them.

Fiery First Date by Pearl_Unplanned:
Tony Stark, billionaire funder of the Avengers, never expected the incredible Steve Rogers, Captain America, to ask him out. No one knows he’s Iron Man, though dating a teammate might make it hard to hide that. And, of course, Tony can’t even enjoy their first date because everything has to go wrong in the meantime.

You’re my date! by Tacuma: Steve Rogers is at at the opening of a very boring exposition, when he feels a hand on his waist.‘I’ll give you a hundred bucks if you pretend to be my date tonight.’ Part of the 50 First Meetings series

First Date by Gothic_Lolita, fiax:
Tony and Steve go on their first date, and Tony falls hard and fast.(Part two of the Coffee Shop AU)

It’s a Date (I had no clue) by @dksartz: Written for a fun challenge on tumblr, an april fools
day ‘fandom bodyswap’ – writers drew art, artists made fics, and I got
inspired! One-shot ficlet.Tony and Steve are friends. Steve loves
Tony and doesn’t know that Tony loves Steve too.  There’s some
insecurity and obliviousness and some confusion discussed on a packed
subway train.