You typically need a high end air rifle if that is what you are going to use for sparrows. The typical ones you buy off the shelf at Wal Mart etc are consistent enough to hit time after time a target that small. So if you don't live in an area that will allow .22 rifles or even a shot gun then you will have to resort to trapping.
I have done business in the past with Andy Troyer, who designed that large V trap that was linked earlier. I was curious about building one about half that size. He said the success rate was a lot lower the smaller the trap. With one that big the bird feel more comfortable going into it. Like others have said the smaller "Blaines" trap will work but it can be hit and miss.