What are you using to check the oil pressure?
The factory oil gauge is just an analog idiot light (search for fake oil pressure on this site)... Over 5psi shows normal.. < 5psi or so shows low...
Now.. assuming you are using some aftermarket gauge, and it is reading acurately, you do have some low oil pressure..
Cold (cool) start is normally 40psi or higher... Once it is warmed up some (not hot) you should be 40psi or higher at 2000 rpms... As it gets hotter, your idle oil pressure may be low, but the 2000 rpms should stay above 40.
Low oil pressure can be the oil pump (bad bypass spring, clogged screen or just a bad pump).. It can also be too thin of oil (5w-30 gives our '92 oil pressure lower than I like, so I run 15-40 synthetic at least during the summer here in southern Arizona)..
Another posibility is worn bearings OR exsessive(sp?) clearence between the pushrods and the rockers..
Bad oil pump or byapass spring in the oil pump is a bad thing.. You can't get to it w/out dropping the pan, and you can't drop the pan w/out pulling the motor. If the screen is dirty one of those flushes that runs the oil backwards might help.. I've also heard of people using bent coat hanger type material through one of the holes in the oil pan to scrape the oil pickup screen.
worn bearings is another rebuild motor time item..
Excessive clearance for the pushrods can be fixed.. You can change the pushrods and rockers w/out rebuilding the motor.. But some people say don't change the pushrods w/out changing the rockers and lifters and cam..
Thicker oil may also help, at least "mask" the issue..
I'm sure you will get other ideas too..
~Mark