Look for a feature/button called 'Favorites' on the replacement remote. That usually will give you the capability to program a list of channels that you can cycle through quickly. The function may also be known by other names.

I took a look at a number of less than $20 remotes and didn't see one with a favorite button. Some of the older One-For-All remotes had this function.

You may have to do some searching to find one.