Lip squeak or knuckle squeak would be my first choice even though I have several calls plus an electronic.
First light, or any time that he is sighted in the vicinity of where you want to shoot him. At night if it is reasonably legal and especially if there is enough town/streetlight to see and shoot him without a spotlight.
Once upon a time I put an arrow into a coyote as it stood by the back bumper of a Mercedes in a driveway off Mulholldand Drive overlooking the lights of Los Angeles. Last year we watched a bitch raise one pup in a vacant lot a few blocks from our house. Coyotes in town is normal in Los Angeles, Seattle, Vancouver, etc. If there is a weedy lot, ravine or brushy patch near where you live, there is a good chance he spends the day there and you may be able to call him to the edge of it.
Someone may give you a bad time re using a .22. For the use you have in mind it is ideal (and from your description of the equipment, it sounds like you can use it.) I killed a good number of coyotes back in the day with .22 long rifle, before I knew it was too small a cartridge. It is not ideal for open range long shooters but for close shots placed precisely, it works well.
Best of luck.
