Look behind your target, you are responsible for anything that comes out of the barrel. I doubt you are going to bring down a Pigeon with a Daisy. Breast shot maybe, head shot maybe.
And something else to remember, somebody always sees what you are doing, as a rule. Right or wrong, if the neighborhood busybody sees you, the man is going to be knocking on your door. Most places it is illegal to use a BB or a pellet gun even if they are classified as a nuisance.
Make sure you know the difference between a wild pigeon and a city pigeon. Wild Pigeons have seasons and some are year round protected.
I have one two word answer "Funnel trap". The thing about a funnel trap is when you get one bird in there it draws the other birds in. I make mine simply, a ground level funnel so they can walk in, emptying into a larger enclosure. It doesn't have to look pretty it just has to work. Chicken wire and cable ties. Cracked Corn and/or/or both old hard bread as bait.