Pick alternatives that are close to the request
If they asked for Tuesday at 2, the most useful alternatives are Tuesday at 12 or 4, then Wednesday at 2. People asked for that time for a reason — stay near it.
Check each alternative against the full appointment length plus any cleanup or travel time you need.
When you're fully booked
Be direct and give a real next step: the first date you do have, or an offer to message them if something opens up (only if you'll actually do that).
Avoid over-apologizing. “I'm booked up that week — my next opening is Monday the 12th at 10” is clear and professional.