* Ευκαίρως (eukairōs): This word means "opportunely," "at the right time," or "seasonably." It carries a connotation of being timely and appropriate, which often overlaps with "on time." This is probably the closest single-word equivalent.
* Έγκαιρα (éngaira): This is the adverbial form of έγκαιρος (éngairos), meaning "timely" or "in good time." It suggests arriving before a deadline or at a suitable moment.
* Πρόγραμμα (prógramma): While not directly translating to "on time," using a phrase like "σύμφωνα με το πρόγραμμα" (sýmfona me to prógramma) – "according to the schedule" – conveys the meaning of being on time.
* Στην ώρα (stin óra): This phrase literally translates to "at the hour" and is a common way to say "on time." It's straightforward and easily understood.
Therefore, depending on the nuance you want to express, εγκαίρως (éngaira) or στην ώρα (stin óra) are likely the best choices. But *eukairōs* is a strong contender if you want to emphasize the appropriateness and suitability of the timing.