Conor's best chance is simply to not box with Mayweather. Try getting in the inside and maul Mayweather with anything like rabbit punches, forearms, elbows, slyly positioning his head for unintentional head butts. Use his size and strength to push Mayweather around. Do everything he can to bend and occasionally break the rules and try to frustrate Mayweather.
I doubt he has the stamina to last doing this, but he should've practiced to throw over 100 punches per round and to constantly keep going forward and not allow Mayweather to back him up at any point, and regardless if he lands or not, give the appearance that he's always the aggressor and outworking Mayweather and therefore is winning the fight