On the bottom of the toilet seat, mark the exact places inside the toilet bowl itself where a fiddle would hit the the underneath side of the seat itself. This can be done with a magic marker sticking up from under the toilet seat pushed up against where the inner part of the bowl begins after the rim.
Make up some wood fiddles like shown in the photo, maybe even curve them a bit to follow the outline of your round toilet bowl.
Make the fiddles deep enough, when attached to the bottom of the toilet seat, to fit snugly alongside the inside rim of the toilet bowl.
Fasten them with self taping stainless steel screws into the bottom of your toilet seat.
Good idea to glass them over, to keep them clean and hygienic, and to keep them from getting wet.
Now put your toilet seat back on the toilet, making sure the fiddles fit snugly alongside the inner rim of the toilet bowl. And Voila! That seat will NOT be able to move. It is kept in place by the two opposing fiddles inside the bowl!