Assuming that you have the fuel sending unit out of the car, take it to the hardware store to fit and purchase what I think is called a tension pin, I called them curl pins but many do not recognize it by that name. In the photo I show two but they are not the correct size. The purpose of the tension pin is to help you locate the exact center of the broken stud so you can drill a pilot hole in it. While at the hardware store, purchase a screw that is of an appropriate thread and length to be the replacement stud. What we are going to do is drill out the old stud and then thread the hole for the new stud.
OK. now that you have the parts needed, take your vacuum cleaner hose (vacuum attached) and insert into the gas tank filler so that you can continuously remove any vapors from the tank and thus work safely. Next, need to tape over the tank hole vacated by the sending unit. Then need to grind the broken stud remains to almost even with the tank surface. Don't want to damage the tank sealing surface. Next, put washers on each of the tank studs and then (with tape removed) reinstall the sending unit. In the sending unit plate empty hole were the stud was, need to insert the tension pin. Needs to be a very tight fit. Since the pin is hollow, it provides a path to drill into the tank where the broken stud remains remain. With as large a drill bit as will fit into the tension pin center, very carefully drill into the stud...slow and steady is the trick. Once you drill through into the tank, stop drilling and remove the sending unit. Some very small metal cuttings may have fallen into the tank but they can be easily removed later with a magnet.
Now, just need enlarge the hole to the proper size so that it can be threaded (tapped) for the new stud. For the new stud, with the screw that you bought, you can leave the head on and screw up into the hole from inside the tank or you can cut the head off and screw the stud in from the tank topside. In either case, need to put a dob of something like JB Weld on the threads where they will touch the tank threads. Let cure overnight and you're done.
Any questions, just let me know.
p.s. My preference would be to insert the screw with head on up from inside the tank. It would make for a stronger fix. Still put a dob of JB Well or something like that up close to the screw (could be a bolt as well) head.