I usually rush RoA before finishing Eye of Watchers. Pick up Ionian Boots along the way with Rylai as the only other big AP item since it adds more CC to everything. Last two items are whatever we might need.
Zrot is never a bad choice if a support is getting to late game. Usually I will always pick a 20% CDR item to pair with it. Athene's is out as Annie can't make use of the passive. Morello isn't bad against healers. IBG can be a good pick for max CDR and situational CC. Frozen Heart is sorta meh unless you're facing an AD heavy comp.
The Zeke's Harbinger and Abyssal Scepter are a good duo for max CDR, decent resistances and decent AP. I rarely run this because Zeke's feels like a laning item and I never think about getting it until late. In many cases I simply pair the Scepter with Portal figuring my 35% CDR is good enough.
I don't think I've ran Warmog's on Annie, but she should hit the 3K health with a fully stacked RoA, Warmog's and Rylai. She won't have any resistances, so something like Portal or GA feels right to pair with it.