What to do in the absence of animal control or shelter resources for a stray?

A few days ago an unfixed dog with a worn collar attached to part of a broken steel cord wandered into my yard. I can't keep seem to find original owners and I can't keep him. The city told me they could only take him if I make and appointment 24 days out. Most shelters are not accepting intake or would take a similarly long time. What do I do? Lots of the shelters keep referring me back to the city and the city is really not helpful. Does anyone have any ideas? He's still pretty young, really sweet, knows some commands, and seems to do well with other dogs and children. I know someone would take him, I just keep striking out in looking for resources.