So, I'm having trouble designing a cleric that can perform archery decently well and also be a decent healer.
The build has to start at 5th level, and it can be most any race.
It's going to be difficult to have both. Archery is feat intensive. Your best bet is war priest.
For a more martial focus, inquisitor may be an option. I'm not sure if hospitaller paladin stacks with holy gun or the paladin archer archetype, but it's worth checking.
On the healing focus side, oracle of life is possible. So is cleric. You WILL be feat starved though. I don't think you'll be able to do these builds without mixing in some fighter levels for feats. If you're multi classing anyway, maybe a dip in the archery monk? It would synergize with a cleric's casting stat.
For Warpriest, what kind of blessings would really help?
I'm thinking possibly 2 Zen Archers levels as a dip, since you get 2 more feats than the fighter dip, and you don't really require Human in order to protect yourself.
I'll also give up (sadly) the Holy Vindicator levels, since then I end up with 9th level spells at 19th? level and +14 BaB.
http://paizo.com/threads/rzs2pgeh?Archer-Cleric-can-it-be-done#1E]
There is some great stuff in that thread. I think Guided Hand is probably the key to the pure classic cleric archer, but there are some great options for archetypes and dips in martial classes.