Right, I don’t know much about coyotes but it seems like Alcatraz Island is too small and too touristy for a coyote to breed there.

Most of the island is off-limits to tourists. It's administered by the National Park Service.

Coyotes are territorial and usually have fairly large ranges. Alcatraz is small, but probably big enough to keep a breeding coyote pair well-fed and mostly out of the way of humans.

But the younguns will need their own territory after a year or so, and needing to cross the Bay to Marin or SF City would be have very low rates of success!