Our 1996 Tracker has a factory spare cover. Because the current wheels are, though still 15", slightly larger the cover doesn't fit well. It has torn and won't go over the tire all of the way. Are any covers made to fit a slightly larger tire that have Tracker in them like the original?

I have to assume, since you say the cover is torn, that it is some sort of a fabric cover - if this is correct, they are available in quite a range of sizes from anywhere that sells 4WD products.  My GV didn't come with a cover, the one I'm using came from Amazon - measure the outer diameter of the wheel/tire assembly and get a cover an inch or so larger.

You probably need to have that custom done.  I think you can find places online that put the Suzuki logo on them, but not sure about “Tracker”