For every state, public park designs are individual. This is due to the designs being commissioned at a local level. So the parks we see in New York are different than the parks designed in California. The commissioning of park designs have been varied in spectrum, from artists to large design agencies. They are chosen for specific park propositions, location and for singular or multiple parks. The parks we see in NYC, which are similar throughout the city are not the same as smaller parks in the suburbs.
For the specific question presented: Who/What company designed the varied assortment of similar parks in the city I could not find a clear answer, but feel free to look through the New York State Parks website.