No-one would bother to ask this. Instead, they would already know what time was convenient for them, and would ask if the partner could meet them at that time. They would mention the actual time when asking.
Saying "Would it be OK for you to meet at my convenience?" is asking someone to promise to meet you at any possible time you later decide. That might be a time he can't meet you, so no reasonable person can agree to make that promise.