Annie's Q refunds the mana if she kills something with it. Unfortunately for support Annie, building Pyromania stacks for free with Q is not nearly as much of an option.
If playing a tanky support, you can bait out the stun. During this time, their ADC will probably attack you; during this time, make sure your ADC attacks their ADC.
Once Annie's stun is down, to restack it, she either has to burn a fair chunk of mana, or wait a pretty long time for E to come off cooldown, or she has to steal some CS. None of these are favourable for her; if you play aggressively when it's down, you can force her to lose mana.
Also, Annie tends to be relatively squishy, especially if her E is not active. She also has no sustain, so while her ADC can heal up poke with lifesteal, Annie lacks that luxury. As Paralytic mentioned, poking her down can force her out of lane rather easily. (Avoid doing this with auto-attacks, though, since her AA range is immense and she will be able to trade back damage.)
It is extremely important to time Annie's Flash. If possible, check her masteries to make sure you know the cooldown on her Flash. Play MUCH safer whenever her Flash is up.
Also, be very wary of when she has 3 stacks built up. She can quickly cast E and then an offensive spell to potentially catch you off-guard.
Toward the endgame, Annie support falls off a bit as she has very little utility. Her AoE stun is a glorified Leona ult that does continuous damage, but she remains squishy. ADCs should avoid duelling with her, since the 1.75 second stun is deadly, but a good support with more utility should be able to outscale in the lategame, provided that there is some itemisation against her damage.