I guess in the Indian context, “timings” would be the appropriate word. After all, everyone in our country talks about “school timings”, “bus timings” and “train timings”. A native speaker of English, however, would find both “timing” and “timings” unacceptable. He would prefer to say “Clinic hours”. The word “timing” has nothing to do with duration, and as for the word “timings”, well, you won’t find it listed in most dictionaries. It is a word that we Indians have coined.