Shaquille O’Neal campaigning for a role in the Avengers is kind of a gutsy move after his last failed attempt at playing a superhero in DC’s Steel. There’s always a chance to be redemptive though, and if the MCU holds fast to the Infinity line there could be another role with Shaq’s name on it. After all as a lot of comic book fans know there were three main parts of the Infinity series that had to do with the gauntlet first and then the different aspects of Adam Warlock. There was the Infinity Gauntlet, then the Infinity War, and then the Infinity Crusade. Each one of these brought together a massive number of heroes, which could be possible in the upcoming years since Marvel now owns 21st Century Fox and all its properties.
In the Infinity Crusade there was a black character named Max, though I don’t know much more about him other than the fact that he’s extremely durable and can alter his size seemingly at will. He did take a full on punch from She-hulk and didn’t blink, so he’s at least tough enough to stand with the heroes and do some damage. But the character I’m recalling was suffering from amnesia at the time and couldn’t remember much. He wasn’t much of a memorable character up to that point unless you’d followed his back story, but he could be the one that Shaq was allowed to play. Of course there are other big characters that Shaq might be suited for, though I don’t know if a lot of them would be with the Avengers.
As for beating up on RDJ as he claims he would want to do, he’d have to find a powerful enough character to counter not just the Iron Man suit but Tony’s intelligence as well, and that’s not an easy task. The reason why Iron Man is so tough is that he’s almost always got a contingency plan and he’s super smart on top of it. Plus the Iron Man suit is like a portable tank that can protect the wearer and allow them to inflict massive amounts of damage on their enemies. Thanks to the Hulkbuster armor Tony was even able to put the green goliath down for the count in Age of Ultron, and that’s no easy task. He’s even gone toe to toe with Thor and Captain America and ended up giving just as good as he got at one point. In Civil War it’s easy to believe that he could have won the fight had Bucky not been there.
But all that aside, Shaq’s only impediment from that point on would be his acting ability. The commercials he’s done aren’t enough to prove that he’s capable of stepping into this kind of role just yet, but his role in Grown Ups 2 was at least convincing enough to think that it could be done with some extra work. The MCU has movies planned for the next several years, so it’s possible he could find his way into one at some point.