I am assuming that you don't want to use a bunch of pesticides or you would have already done so.
If you live in town you could go out to the country and collect toads and lizards, or pay some youngster to do it for you and provide a habitat for them in your courtyard.
I am always careful of chemicals I use because we have a large toad and lizard population (in the country) and I know they are keeping my insect population down.
What would happen to them in the winter (in NY) though I don't know.

Carol --

Are you talking about deer flies? Small, black and triangular in shape when they land? If so try the link below. I made a trap from an old flower pot and put it over a 3' wooden dowel I taped to the lift lever on my mower. After mowing for two hours I had 42 stuck to my trap. Amazing how well this worked. Happy hunting!!

Here is a link that might be useful: deer fly trap