We've got a collapsible cooler that we've used as a carry on before: it has a nice strap, outer pockets for other stuff and is perfect for our kids to carry their stuff in when we fly. (We got our at CVS and it's made by Thermos I believe)
But something else we've done is pack it inside our checked luggage. Just put the empty cooler (not folded up) into the empty suitcase. This way it just sort of forms a divided area in your bag. You can pack it full of undies, socks and tshirts -- or breakables, since it's plastic lined -- and then pack everything else around it and you don't waste any space. Then when you get where you're going, take everything out of it and you've got your cooler.