They're both correct.
1) Please check your schedule and let me know a date and time that is convenient to you.
This is a rather formal set phrase which is used mainly in written English and in business and administrative contexts.
2) Please check your schedule and let me know a date and time that is convenient for you.
This is standard English. It can be used in any context, in spoken or written English, either in formal or more informal context. This is the one which you will find more useful.