You can make anything work with enough modification and fab work, but you'd need one from the older midsize Blazers to work with the 1st gen body style, something from the later Blazer probably won't match up, at least in terms of the brackets.
You might want to try the tire carrier from the more similar Bronco II.
They have both been mounted on lots of other vehicles, from pickups to minivans and other SUVs, so it certainly is possible. The hard part is fabricating the reinforcement inside the body for the brackets to mount to. They don't just bolt on to the sheet metal, you actually have to have some thick, strong metal solidly mounted inside the rear quarter panel for the brackets to mount to. Even more so if you're planning to use it to carry a 29" or larger tire.