Dalry Park is in the Tullycarnet/Gilnahirk pocket off the King’s Road. That wider Tullycarnet housing estate was laid out by the Northern Ireland Housing Trust between 1966 and 1970, with final phases completed in the early 1970s by the new Housing Executive—so Dalry Park’s street name approval falls in that late-1960s window. Contemporary council and transport mapping for the area shows the street in place by the time those plans were drawn up.
The micro-area uses a Scottish placename theme—nearby streets include Kinross Avenue and Granton Park—and Belfast has a long tradition of adopting Scottish names for streets. “Dalry” matches that theme (there’s a Dalry in Edinburgh and one in North Ayrshire), and the word itself is commonly explained from Scottish Gaelic dail + ruigh (“haugh/field at the slope”). In short, “Dalry Park” was almost certainly chosen to continue the Scottish naming motif used across that 1960s estate.