I had a Buick with the 3.8 that had this problem with the water pump. I replaced the pump, and shortly after, the new one started leaking. Turned out to be the radiator cap. It wasn't releasing, and when some coolant boiled (usually a few minutes after shutdown, when it wasn't circulating), pressure was released by spewing coolant from the weep hole.
Replaced the cap, and the new pump lasted another 50k+ miles.