I used to fix the old "non-demountable" ATC90 tires by using burn on patches, on the outside of the tire. Basically, you grind down the area of the leak to get the rubber pretty smooth, then apply the patch using flammable glue (follow the directions...you have to let the stuff dry before applying the patch). After it's on, you paint the gray edge of the patch with the glue, then light it on fire. Immediately blow it out, then relight, then blow out, then relight....until it doesn't relight. Let it cool completely before inflating the tire.
Really bad cuts can be sewed shut with fishing line and sailmakers needles, then hot patched over the repair. I rode a lot of miles on those external patched tires!
If your tire has cords under the tread, you can use a plug repair kit. If it's just rubber (like the original ATC tires) the plug kit will just tear out.