I would request you to refer to How to apply for a second original copy of birth certificate, as this detailed resource has almost all the help that you are looking for.
Also, as informed by you, if your place does not have a municipal corporation, you can visit the other municipal corporation that is nearest to your place and follow their instructions.
Please don't worry. You should know that there maybe many who have been there in your place. Just visit the nearest one and get your work done.