Whether or not you are a convicted felon is not a question that insurance companies will ask you. The simple fact is that everyone who drives a car in this country is required, by law, to have auto insurance. Furthermore, auto insurance companies are not concerned with your criminal history unless that history involves either your credit rating or your driving history. If you have applied for coverage with a company that refused coverage on the grounds of your being a convicted felon, try another company. While you are at it, go ahead and report that insurer to the Better Business Bureau.
If you have not had car insurance for a while, some companies will deny coverage on the grounds that you are a high risk. This label gets added to anyone's record if they allow car insurance to lapse or are charged with the crime of driving without proof of insurance. If you are convicted of that crime too many times, you will be considered a habitual offender, and that could make it more difficult to get coverage.
Most people do not realize that there are a lot of convicted felons in this country. If insurance companies could deny coverage on those grounds, it would make it virtually impossible for a felon to stick to the "straight and narrow," as they would be legally allowed to drive a car through no fault of their own.
To get car insurance, start right here on this site. Get a free car insurance quote and check out the comparisons that you are provided with. As you will see as you go through the process, there is not a single question which pertains to a criminal past, outside of questions regarding your specific driving record. What you will be asked about is your driving history, but even those questions, again by law, cannot delve more than 3 years into your driving history.
The problem you are going to face is that, since you do not currently have auto insurance, your rates will be much higher than if you were simply changing from one company to another. For the insurance company, any period of time that you have gone without insurance, even if you were not driving during that period, counts against you. There is no way to avoid this extra cost, but you can minimize it by taking out a 6 month policy. You'll have to pay the high risk premiums for 6 months, but as long as you do not allow your insurance to lapse at the end of the 6y months, your rates will return to normal.
If you're still unable to get a policy, try contacting local car insurance agents to see if they can find an insurer for you.