If your varifocal glasses are made of standard plastic lenses and there is no an anti-reflection coating or scratch- resistent coating on the lenses, it is possible to have your lenses tinted. And if you want it to block UV rays like sunglasses, you should add UV protection to your lenses after being tinted.
Generally speaking, it can be tinted as long as there is no hard coating on your lenses. However, you should consult your opticial store to see whether they can do it for you. If they can't, you should get a new pair of sunglasses.