I have a 150 square foot bedroom over an uninsulated garage which is difficult to cool. It is also farthest from the central AC unit. Would insulating the garage ceiling help to cool the room?

You didn't say, but I assume that the garage gets hot, right? If that is so, then insulating the garage ceiling to keep the heat out of the bedroom above is a good idea.
Also, do the air conditioning ducts run through the garage ceiling? If so, you might want to insulate them if they're not already insulated.