Tire shake comes in different varieties, so by your posts I am guesing that you could maybe use more air in the tires.
A Dead Hook Tire Shake is different than a Bust them loose Tire Shake.
Dead Hook Shake can be lessened by additional air pressure, more sidewall screws or beadlocks, Decreasing rear suspension tire hit or anti-squat.
Whatever you do don't have the wheelie bars down low if you are tire shaking. The wheelie brs will lift the already square tires and really make a mess of things. You do not ever want a Dead Hook in a high horsepowered car. You need some small amount of wheel speed to be greater than the distance travled. In short you want to lay down some tracks and if you aren't you need to do some adjusting of something until you do.
Tire shake cam be magnified by so many different things. Let us assume you have an automatic car. Look for anything loose in the suspension, bushings, worn heim joints, worn anti-roll bar parts, worn bolts or bolt holes in your suspension brackets, Look at all welds near where any suspension bracket is creating a force or tirque load. Look at the welds for a little rust trail coming from them. If you see that the weld is busted lose or is partly busted loose and needs ground down and re-welded. Also in the rear frame ares look for cracks also found by little rust trails.
Ed