Or, you can emphasize that they can call at a time when it would be convenient for them: You can call me whenever it's convenient for you. The phrase "at your convenience" is sometimes used: You can call me at your convenience.

Do it in your most convenient time meaning?

Whenever one wishes; also, as soon as one can. For example, Pick up the car any time, at your convenience, or We need that drawing very soon, so please finish it at your earliest convenience. The use of convenience in the sense of “ease” or “absence of trouble” dates from about 1700.

When would be a convenient time meaning?

adjective. A convenient time to do something, for example to meet someone, is a time when you are free to do it or would like to do it. She will try to arrange a mutually convenient time and place for an interview.