I would use Epoxy. Try to counter sink the hole so there is more surface for the epoxy to adhere to. Mix the two part epoxy - if it is too runny, just wait a bit until it just begins to harden or thicken up and put some on the hole. You may wish to add some more after the intial application hardens. My bet is it will hold very nicely.
I had a Washing Machine, tub type, and it was leaking. I pulled the agitator and the Basket, (the part that spins around in the spin cycle). I could see what appeared to be a "bubble" looking piece of rust on the tank. I gave it a flick with a screwdriver and the bubble broke loose from the tank, leaving a pretty good sized hole (about the size of the ink barrel of a cheapo ball point pen). With nothing to loose, I got a very large drill bit and using it as a countersink, I countersunk the hole and put epoxy in it. It lasted for another 6-7 years - Epoxy is tough stuff.