Erwin, you might want to look into the insured motorist pool in NY state. Can't say if they still offer it, but when I was growing up there (Rochester area), I was able to get basic liability coverage for much cheaper than my parents could add me to their policy. The pool is comprised of higher risk people (high schoolers, first time drivers, first time insured, and others that can't normally afford insurance, including people with too many tickets), which are offered lower premium rates than they'd normally qualify for, and which every insurance company in NY state is required to offer a certain percentage of their written policies in.
Back then, I was able to score liability for $350/year, as a 17 year old male, first time driver, in a state that has no-fault insurance. Having driver's education saved me 10%, and being on the honor roll in my high school scored me another 10% savings. 🙂