crow hunting help

For crows and that price point I would suggest a used .22 magnum rifle (powder burner). It would give you the distance accuracy and power needed to dispatch them easily. In an air rifle I haven't seen much at that price that I would rely on. In pre-charged pneumatics a used Benjamin discovery with a pump might be found at $300 if you're lucky. I'm not a springer fan, but you can get a gamo for 100. Crows are smart(Google crows and face recognition) and you'll likely only get one shot at close range. Also check out Ted's YouTube video of air rifle crow hunting-ricochet investigation. Get one and dissect it in plain sight of the murder (that's the name for a group of crows) and maybe they'll bypass your area like they did his! I've hunted them and a trick I used was to kill one and make sure it was left in the open plainly visible, make sure you are completely hidden and pick them off as they come to investigate. Good luck. 
 
I agree with plinker. At that price point you will be looking at a .177 multipump or springer and not a very high quality one. But I dont want to make any assumptions so I will ask, how close can you get to these crows? And how much time are you willing to invest in target practice to get comfortable enough with the rifle to maintain accuracy at the range you will be shooting?
 
Start checking Cl for a decent pellet rifle used. Most likely you will end up with a break barrel. BUT you might find a nice PCP that someone is getting rid of. Lots of times, the people are negotiable and are willing to trade for other things you might not be using. 

I traded a FLY TYING kit for my first Benjamin Trail NP .177. The kit cost me $50 and I had made a few flies with it. Gun was $300 and he had a $300 scope on it at the time. Plus I got a couple hundred dollars worth of pellets. \\\

Deals are out there and people do not see the value in things after they loose interest in them. 
 
Dan25 has the right idea if you are going for effectiveness and are not in a noise restricted area. You can find a 20 or 12 gauge single barrel shotgun for around a hundred dollars. Cheap ammo will to the trick under 50 meters and it is about 25 cents a round...but you can get crows down almost every shot. Pellet guns (especially high performance ones) are precision machines designed for sniper like tactics. A solid shotgun is more like a heavy artillery piece for birds and can be effective without having to use rocket science (wind doping, drop, placement, humidity, and a 150 dollar scope). I LOVE taking small game with my Marauder .25 but it is still a chance of circumstances and technique. If I have an hour to get out in the woods and fill my bag with 5 squirrel for the dinner plate I'm using my 20 gauge. This might go against the grain on such a site, it is the truth as I see it. You can get a decent spring gun for 200 dollars but with open sites you are going to need luck and skill and you are still probably going to miss a few. With a 100 dollar shotgun you need 20 dollars of shells and keep the beed on them and you will be having crow pie in short order.