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This is usually because the coyote wants to play with the dog. Coyotes are actually very playful animals. They do like to play and they seem to play games with the foxhounds when we are out hunting, leading them on a chase, going slow until the hounds get close, then taking off. They are not evil, vicious animals.
I can't imagine one attacking a man, unless it was cornered or trapped, or rabid. They are generally shy and timid.
For a better understanding of fox and coyotes, the Rita Mae Brown fox hunting mystery series is a fun series to read. Not a lot about coyotes as it's mainly written in fox country but there's enough about coyotes to gain a better understanding than most non-hunting folks have. Plus, the books are entertaining. Great for animal lovers.
Again, if you would like to relocate your coyotes, contact your local fox hunting club. There's a list at MFHA.com. Fox hunters are really into saving the coyotes and foxes. They would much prefer to trap/relocate your predators than to see them shot. The fox hunting in the US is no-kill. It's just for fun, just chasing and never killing. ( I have rarely seen a jackrabbit killed when it practically committed suicide by jumping into the mouth of a beagle but for the most part the fox-hunting ( to include all English style hunting with hounds and horses coyote/fox/jackrabbit no-kill but not coon or lion hunting)