I say maybe Cooney get's a moment of rocking tyson with a left square on the jaw like Bruno did for his moment but still getting swarmed and TKO'd in the mid rounds.
Tyson in 1 possibly 2 rounds. These slow easy to read heavies are the types he slaughters and looks like an all time great heavyweight. Cooney does not have the defense to deal with that Tyson speed and energy burst. there would be 2 or 3 big punches coming all within about a second from Mike and Cooney is not avoiding anything more than 1 of them. Punches 2 and 3 will do a number on him and what bag of tricks did Cooney ever show that would allow him to kill time off the clock against an opponent like this when hurt?
Cooney reminds me a lot 'psychologically' of Bomber Bruno. So the Tyson in five, having been stunned once or twice on the way, would seem a fair call.
If Cooney stepped into the ring determined to fire that left and 'give it a go', then he would of shown more 'mental strength' than he ever did. I suspect like his fight with Holmes, he would of lost before a punch was thrown, and he would of gone into the ring with the sole intention of not being 'embarrassed'.
Gerry Cooney was very protected by Mike Jones and Victor Valle. With that said, they knew he was 'chinny'. Just ask Eddie Davis. But, for 2-Rounds he may have banged Mike around pretty good with the left hook, much like Razor Ruddock did. But somewhere in the 3rd Round, Gerry would go spaghetti-legged.
Tyson would be wary of Cooney's power, but not afraid. Cooney would be afraid of the pressure and demands of beating "The baddest man on the planet" and, as TBooze noted, find a way to psych himself to a soft spot on the canvas pretty early. Lord only knows what Cooney could have accomplished if he wasn't so utterly self-defeating.