Located opposite St Mary's Church in Elizabeth Street, the hitching rings were used by people going to Mass to tie up their horses. They form part of the wall on the park oval. These hitching rings are a reminder of the time when many members of St Mary's congregation arrived on horseback or in a horse-drawn vehicle. The metal rings were made by Robert Campbell, a blacksmith whose shop was in Brisbane Street in the Top of Town.
The park was named after Monsignor Timothy Molony who became Parish priest in 1951, and remained there for 25 years.