My child was given a used Xtreme Tantrum 90cc. I rode it to check it out. It is very fast, even with an adult (130lbs) on it. Worried that it felt very tippy in turns.

It has very rounded tires (think donut) - would changing the tire to a wider, lower profile tire help?

What would you suggest to make it safer before I give it to my child?

 

Get some of those screw on extenders off of ebay. That'll make it wider.
Just changing the tires won't help much.