It's in front of Victoria Flats, and at the top of Chatham Path.
It was built as part of the construction of the Victoria Hospital Maternity Block (today's Victoria Flats). The newspaper report about the construction of the Maternity Block also mentions the construction of the tennis court:
It has been decided not to add the wing to the present hospital building, but to erect a separate block on a site further west. To make this possible it is necessary to cut away part of the hill [and] dump the earth on the other side of Barker Road and build a retaining wall against it. On the new site so created a tennis court will be laid out, [...]