A dissertation on why Poppy support is strong
Bandit + Passive
Bandit + Passive
Passive also procs 
I did poppy support and it was actually very nice.
My poppy support build

Found it to work quite well.
Your not very strong but you get considerably tanky and you peel amazingly and with everything you offer your ADC they do well.
Why build AP? Because it goes with your W ability which you use a lot to protect the carry.. ALWAYS BE NEAR THE CARRY AND YOU WILL SAVE THEM EVERY TIME WITH YOUR W
the buckler also uses both hydras
I want to see hit-and-run poppy:

Pop w, run up really fast, activate hydra, toss a mean freaking buckler
Yeah, Jungle Poppy seems rather abysmal and I've not tried top yet, but I'd imagine that you'd get better CC and damage from Gnar.
So all I have left is support Poppy.