Is there a permanent (non-emergency) patch/boot for a tire, NOT for a tube?
It is not clear from your answer if "tiny hole" means your tubeless sealant has a problem sealing it or that your inner tube is bulging through.

If the hole is really tiny, you can patch it with a tube patch. There are also dedicated tubeless tyre patches that are the same, but bigger and thicker. If the hole is really "tiny", they should work. If not, they could bulge through as well.

If the hole is bigger it can be sewn together. That can be then covered with a patch from the inside and with a polyurethane glue from the outside.


                
            

Only you can assess how dangerous that particular hole is and non-emergency such a repair can be. The higher pressures you use the worse it could be. Thin road tyres with 100 PSI and thick MTB tyres with 20 PSI are something completely different.