How about Hamel Memorial DOG park?
Hamel Memorial Park is off Clyde Fant Parkway. On the Red River and river trail, the spot is ideal because it is a big open space, it is by the water, it already has infrastructure in place (entrance & parking), it is at the end of the recreational trail that can end up as the destination spot for dogs and their owners.
I read in the Times that the area has problems with incidents of indecent behavior. A dog park eliminates that problem!
Some additions to the dog park may include a hose for watering off sandy dogs (and their owners), poop bag dispensers, trash cans, and perhaps a fence of some sort. A posted sign with city ordinance stating owners must keep dog under control, pick up poop, state potential fines, etc.