Same here, a pup has no chance with coyotes. It's been a few years since it happened but a cousin had several little house dogs. She'd sit on her porch sometimes and let the dogs play in the yard. One afternoon a coyote ran out of the woods, grabbed one and was gone before she could react. Broad daylight with her 20ft away! That's one of several reasons it's open season on coyotes in my state, by any means necessary!
After the little dog episode everyone for miles around shut their dogs up for a month. Her husband soaked meat in antifreeze and drove around dropping pieces of it beside roads in every direction. Don't know how many he killed but I rarely heard them for a couple years. Perfectly legal here... traps, poison or shoot on sight.
Hope the pup gets found quickly...