Longbow is a martial weapon, and clerics only get simple.
The only way I can think of to get multiple ranged attacks in a round is to have multiple weapons. ie, two pre-loaded Slings. Which works according to the rules, as far as I can gather. I could also have a sling and a light crossbow, fire the sling, drop the sling, and fire the light crossbow.
Loading takes forever anyway, though.
I was considering wielding a longspear, which gives me multiple attacks, but no matter what I'd have to drop my shield.