You can say: “Sono stanco dei bambini che corrono per casa” or “Non ce la faccio più dei bambini che corrono per casa”, or even “Non ne posso più dei piccoli (or bambini) che corrono per casa.”
Generally you can translate “I’m done with something” with “Non ce la faccio più di...” which literally means “I can’t do it anymore...” or alternatively “sono stanco di...” which means “I’m tired of...”
If you were translating it literally from English, it would be “Io sono fatto con...” which actually means “I’m made of...”, so it has a completely different meaning. Also, remember that the Italian translation is very informal, so be careful when you use it!
If you have more doubts or other expressions to translate, send me a message. I’m happy to help :)