What auto insurance companies will insure someone with a restricted/privileged license?

I currently have a restricted license (meaning I can only drive to work and school in between certain hours because my full license was suspended), and I was trying to switch auto insurance companies to save money. It was AllState or State Farm that I called, and they told me they could get me a much cheaper rate, but couldn't insure me because my license is coming up as suspended. Apparently the DMV doesn't recognized my license as privileged, although I have all of the court papers to prove that I have a privileged license and am currently insured. Does anyone have any suggestions? Like any specific companies that could insure me for cheaper rates, given my poor driving record? Thanks!