I've used this cheap red dot:

https://www.amazon.com/gp/aw/d/B019MN7N5U

and this mount:

https://www.amazon.com/gp/aw/d/B01IWPI3EY

every day over the past year, for squirrel hunting, and haven't had to re-zero it even once. And that's with about 2000 pellets shot through my Gamo.