If you want to color your hair after perming then you should atleast wait for two weeks. Use your own discretion. Look at the strands closely in the mirror. If they look raw or have split ends, then you might have to wait longer to get it colored. It is better to wait for some time after perming as it really damages your hair.
It also depends on the condition of the hair. As long as everything is in good shape, about a week would do but the least amount of time you can wait is 24 hrs.