What kind of air gun/bb gun?
Get them while they are setting in the trees doing their mate song/dance. If you have male Starling thats taken cavity he will set somewhere close singing for mate. That's the time to get him. Use the shotgun. I would also use old pillow on the wooden rest when you shoot the rifle will sink in the pillow creating soft steady rest for your rifle. You can adjust the scope on the barrel some to get the scope closer to your eye. Or if you rifle not classic or antique you can cut the stock down and move the butt plate forward making it shorter to fit your shoulder to eye