wrote about on Monday which is on the Yarra in Birrarung Marr.
This one is further along the river near the Morell Bridge.
I've been able to find some more details thanks to this website created by the Cultural Heritage Unit at the University of Melbourne.
In 1936, the area between the Yarra River and Batman Avenue was named Stapley Parade Reserve, after Councillor Frank Stapley, who represented the Albert Ward from 1898 to 1939 and served as mayor from 1917 to 1918.
It goes on to say that two identical fountains were constructed at either end of the reserve and were engraved 'Stapley Ave'. Clearly they are now engraved 'Stapley Parade' but presumably still mark the extent of the Stapley Parade Reserve.
I've looked at my 1991 Melways and the reserve is not marked and of course the city end of the reserve and Batman Avenue have now been incorporated into the Birrarung Marr park and the Federation Square development.
Another page on the website lists other memorial drinking fountains around Melbourne, including some I have previously written about.