What is causing my low oil pressure in my 99 grand cherokee?

I have a 99 Grand Cherokee V8 with 250,000 miles on it. It still has GREAT power. It has no noticable smoking from the exhaust. No oil leaks at all. Fresh oil change. Lately when I crank it after it has sit for at least 2 hours, you will here a tapping sound (not real sure if it's lifter or rod) when you crank it. I noticed the oil pressure will be running pretty low during this time. After driving it for 15-30 minutes, usually the pressure will go up fine and stay and the tapping will go away. Maybe some of you mechanics can help me out. Do you think that it is my oil pump getting weak? or maybe something else?