You can use "any" and "convenient" in the same sentence, but not the way you wrote it.
You can tell someone they can call you whenever they want by saying "at any time" (sometimes this is shortened to "anytime"):
You can call me at any time.
You can call me anytime.
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.
If I were to combine the two, I'd probably put the "any time" part first:
You can call me anytime that's convenient for you.
If the part about convenience goes first, then anytime can be used for emphasis:
You can call me at your convenience – anytime, day or night.
As for may vs. can, may is probably the more correct word to use (at least in a more formal sense), but can might sound more friendly in informal contexts. But you could say the sentence without using either one:
Call me any time it's convenient.
Or, if you really want to be brief, this works, too:
Call me anytime!
"Classical Mechanics is a well known field of Mathematics." Do you even listen to yourself...? – Najib Idrissi 19 hours ago
The user "Najib Idrissi" asks the author of the sentence Classical Mechanics is a well known field of Mathematics. to read that statement for themselves. Najib makes sure that the author will realize the scientific mistake in that sentence and, in short, "will come to their senses."
It's like your friend has told you something very oddly wrong, and you didn't expect him to say so. You tell him/her to listen to himself/herself, so that s/he will realize the mistake they've made. In this case, it seems very rudimentary to the mathematicians that "classical mechanics" are a physics' subject, and hardly related to math. So, "well known", as it means that "many are familiar with it being a part of mathematics" seems a very idiotic expression to them, as if the author didn't know what they were typing, or simply, talking about.
If you ask me, there is a bit of negative connotation in this sentence, but it wouldn't be considered as offensive. (As "offensive" is too strong for it)
In fact, the expression "listen to yourself" is commonly used in the area of philosophy when there's a speak of art of communicating between humans.
philosophy reference 1
philosophy reference 2
The third
And this is a nice example of a similar usage. (Though it contains the expression and not the exact question)
in Google books
Best Answer
Here, "once more", "again", or "another time" would all work. "For another time", though, suggests that they can only listen to it at a time that is not the present: they're saving it for later. (Phrased the way it is in the question, it doesn't really make any sense, but that would be the closest to the usual understanding.)