Hi.
I'm assuming that your parents put a lot pressure on you when you were dating the first black guy--so much so that you felt you had to break up with him.
You have several choices. You can try to make it work this time. It's possible that things will be different, that your parents will become more understanding and accepting of your wishes to date whomever you please, but it is probably unlikely. Only you can gage how deeply entrenched your parent's feelings are about you dating black guys and how likely they are to be swayed.
If you are pretty sure that your parents will never go for it, the other option would be to wait until you are in college or otherwise out of your parents' household to date whom you wish. It might be less stressful for you and your future partners.
However, you're not alone. There are plenty of other girls who do not have their parents' permission to date someone of a different race--not to mention religion, nationality or class. You might try looking on the relationships and sex board for additional support.
Take care.