This is a matter of State law not federa llaw. You can apply for gun privileges. Usually there is an area on the form to explain your unique situation. Assuming you are not under alcohol treatment for alcohol dependency and your crime did not involve the use of a gun, give it a shot. If you are denied, you would be in no worse position than you are now.
Bruce A. Brennan
YOU CANNOT OWN OR POSSESS FIREARMS!!!
This question is NOT simply one of state law. Federal law prohibits a convicted felon of possessing a firearm unless they have had their rights restored under state law.
The only way to do that is to petition the Governor's office for restoration of civil rights. This is extremely unlikely to happen. Until it does be aware that you are violating federal law if you possess any firearm.
Disclaimer: This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.