I don't have any time on other activities

on 改成for 就可以了，你可以加一些东西，使句子更简洁，如
I have no time on other activities。因为no 就是not any的意思

I don't have any time on any other activities
我没有时间参加其他任何活动

完全中国式英语的感觉……汗~

on ---- for

这个句子是正确的。

you can say :

I have no time on other activities.