How do you convince your parents to let you get your Industrial pierced you have begged and they keep saying no I have my belly pierced and they agreed to that?

It couldn't hurt to go online and learn all you can about proper piercing techniques and aftercare... That would be smart for you to do in the mean time anyway.

In order to try to successfully convince them to change their minds, you need to know why they are objecting in the first place. For example, I don't know if their logic is "We said you could have one piercing, and you used it on a belly button piercing" or "belly buttons are hidden whereas industrials are not, and we don't want her to have trouble at job interviews and so forth" or what. If you know the REASON for their objection, then you can formulate your rebuttal such that it addresses their specific concerns. "You let me have my belly pierced, so why not an industrial too!?" is not a good argument, that's for sure.

It might also help to include them in the process. Even if you know they would say no, at least OFFER to let them come with you when you do it and meet the piercer, etc. In fact, if you have a good piercer, it would probably only be a good thing if your parents met him/her and saw how clean and sterile and professional everything was at his/her studio. (This is, of course, assuming you'd find a good piercer with a good studio!)