Cheng shin knobbys, very slighty bigger but will easily fit your rim (they are 20x7-8), from rockymountainatv, $19 each and they're a good tire.You won't find anything close to that cheap, plus they're a decent tire.these are 1" larger which is 1/2" higher. same width and rim size.

 

If the tires are not worn out.. I think you are dealing with an inherrent problem of most all ATV designs have. There is an issue of weight distribution. In most cases, teh weight will be concentrated on teh rear of the quad, and that unloads the front tires to the point thwere they sort of skip around corners rather than diggin in and turning. On big quads, you can get tires that have large knobbies along the side edge that helps fix the problem, but not sure if they are available for minis.

A good way to tell is to stand on teh pegs and lean forward while turning.. if it significantly changes the cornering characteristics, that is what you are dealing with... It is called a "push" condition in NASCAR circles, and they compensate with wedge that will load the weight more on a particular corner.