Amumu support is INSANELY easy to bully, since he lacks any way to do anything to the enemy laners without going all-in. I've done it for lulz. The idea was to start Doran's Shield, level tantrum first and take the defensive mastery for less damage on autos to make it so level 1 amumu took something goofy like 15 less damage from autos, then to go ham on the enemy...
It didn't work. His early game is too awful to go ham and he can't stop savvy enemies from steamrolling over him and his adc. If you somehow survived early without giving up TOO much of a lead it might work due to how good his teamfight ult is, but it still seems like there are better picks. Try it for fun though and see how it goes. I can't really give you crap, I've played support Sion quite a few times.
[slayer-jinx-wink]