sadly, one of the best things to do is quietly serve out your punishment, and not push too hard to get it removed. However, behave responsibly at every chance you get, it will take a while, but this is the best way. It is hard to gain trust, but very easy to lose it.
To gain your parent's trust again, you need to be obedient. Listen and obey what they have to tell you while trying to talk to them about how they feel. Talk to one of them or get someone to do it for you for them to reconsider.