How do you prime an oil pump on a 1992 dodge shadow with the 2.5L engine? The oil pump is still in the car. I do not want to pull the pump back out of the car to prime it. Is there any way to do it with out taking it out?
Yup. You'll need to remove the timing belt from the intermediate shaft sprocket so you can turn that sprocket. It turns the distributor too so be sure to retime it correctly when you're done. You might find it easier to just crank the engine with the starter relay. If you don't use the ignition switch, the injectors won't spray raw fuel, the plugs won't fire, and the engine won't start.
If you just completed a total rebuild, the assembly lube on the bearings and cylinder walls will provide sufficient lubrication until oil pressure comes up. If you just replaced the oil pump, oil should have drained out of the passages leaving the pump. That's good. If oil remained there, the pump would not be able to push the air out and draw new oil up from the pan.