I don't care for pump action airguns (unless it is a single-stroke pump-action), because the point of aim will vary depending on the number of pumps you put into the shot. At least with single-stroke guns, like the Gamo Compact single-stroke target pistol (which is more accurate than many air-rifles I've tested), you have a "calibrated" power level that doesn't affect point of aim.

Here's a link to the Gamo Compact air pistol.

Gamo Compact Air Pistol

This is absolutely the most accurate airpistol I have ever tested. It is not extremely powerful (400 fps in .177 cal), but it truly is capable of pinpoint accuracy. It has an excellent adjustable target trigger which is very important in obtaining top accuracy.
I see they are about $225 now. I bought mine several years ago at a Turners Outdoorsman store in Pasadena for a little over $100. Amazing airgun for the money.