Budget budget budget.
You said (finally) that you'd like to say under $300, but don't seem to be committed to this budget.
What's the REAL budget that you're really willing to spend, realistically, really? Because it's all about budget - you get what you pay for, generally.
Keep in mind that, unlike squirrels, pigeons & doves are extremely fragile and thin skinned (as are most birds) - you only need something shooting a .177 pellet in the 400-600 fps range, but if you want a little more versatility, get something that shoots them in the 600-900 fps range, but then you tradeoff some quietness to get this power.
I have killed both pigeons & doves with a Beeman P3 / Weirauch HW 40 PCA pistol at around 400 fps. Get within about 8 yards, and it's money in the bank.
But is $300 the real budget or not? If you can swing it, you can get a much better gun than on a lower budget, which will last longer, shoot more accurately, be more quiet, and look nicer.
Accuracy is THE most important consideration (but most all modern pellet rifles will be pretty accurate). Quietness *may* be a close 2nd, depending on how close your neighbors are, and how easily perturbed they are. Without knowing more, someone mentioned the Beeman R7 (R seven) is an excellent choice for your purpose, but you'd probably have to buy used to get under $300.
http://www.google.com/products?q=be...a=X&oi=product_result_group&resnum=1&ct=title
Elmerfudd, I'm with you - I've been saying for years that if Aguila would just make their super colibris accurate / consistent, they'd sell the crap out of them. They're only gonna hold a 1.5" minute of bird group out to about 12 yards, and that's out of a very accurate rifle! (CZ 452). I'd be in hog heaven if the super colibris were made more accurate (say, capable of 0.5" out to 15 yards). Usually I'll get 4 out of 5 within 1" at 10 yards, but then an ammo-induced flier (yes, I'm sure it's not user - induced) will be an inch from the main group - disgusting.