I saw a number of people doing rental mopeds, but almost all of the places I saw renting them were in the tourist coastal areas (St Louis, St Gilles). I expect it can be done pretty easily, although you may have to find a way to get from St Denis to the rental place (there's a rather extensive bus system, Car Jaune, that can get you from St Denis to pretty much any other major spot on the island).
Like a car, you want to be pretty skilled with shifting. Aside from the coastal road, almost all of the roads on the island are extremely twisty and steep.