"On one's time" is a phrase that is commonly used to refer to a person's free time, or their personal time. However, there are several synonyms that can be used in its place, depending on the context. For example, "off-duty" is often used to refer to a break from work or responsibilities, while "leisure time" emphasizes the idea of relaxation and enjoyable activities. Other synonyms include "personal time", "free time", and "downtime". Ultimately, the choice of synonym depends on the intended meaning and tone of the sentence, but all convey the idea of time that is not dedicated to work or other obligations.