For A: Use at any time (not on any time), and don't use of before tomorrow:
Can I take this coach at any time tomorrow?
For B: The sentence is fine:
Can I take this coach anytime tomorrow?
For C: The sentence sounds like fluent, idiomatic English.
For D: Again, don't use of before tomorrow; also, it's generally in the afternoon, not on the afternoon:
We will arrive at the pier in the afternoon tomorrow.
Although we could also word that as:
We will arrive at the pier tomorrow afternoon.
and we'd use the preposition on if we were using the name of a specific day:
We will arrive at the pier on Tuesday afternoon.
We will arrive at the pier in the afternoon on Tuesday.
(As a footnote, I wouldn't argue that "on the afternoon of tomorrow" is ungrammatical, it's just clunky and I'd recommend avoiding it.)