Kindly getting rid of wild birds *Update*

get netting or get a barn cat a predator around their new food supply should teach them
 

Use a treadle  (SP) feeder-one where the chicken steps on a platform which opens the feeder so chickens can eat.  As soon as the chicken hops off the feeder closes.  Unfortunately, squirrels can learn to open a treadle feeder.

I had a friend who made what I can only describe as a small tent around her feeder.  At first she left the zipper-door open and as the chickens learned to go inside she closed the door inch by inch until the opening was small enough for a chicken to squeeze through.

I don't think you need worry about killing baby birds. For nearly all species, nesting season is pretty much finished.

Yep, most of the nesting season is over now....besides, you don't want wild birds brining in lice & mites etc. to your chickens. Put a feeder for birds up somewhere outside away from your chickens they'll forgive you.

I'd second the treadle feeder suggestion.  You can find plans to make one in my sig. line and commercial versions are also available.   There are other auto-feeder designs that are easier and cheaper to construct.   The trigger/lever activated bucket feeders are well reviewed and can be seen in this thread.  Also see post #10 & #13 in this thread for a very cleaver auto-feeder design.  I would point out that the success of these types of feeders depends on training the chickens to use them.

I had birds nesting in the loft and the easy answer was to darken the loft window! The birds needed more light and left. I also hang CDs in the pop door and over the run. That seems to reduce the sparrow population a good deal.