Ah You, who joined the club from Canterbury in 2010, has signed a one-year extension, while Cooney has agreed to remain for an additional two years.
Connacht CEO Tom Sears told the club's official website: "I'm very pleased that Rodney and JP have committed their immediate futures with Connacht Rugby.
"Both young props have displayed destructive scrummaging and ball-carrying skill this season and I'm looking forward to watching them develop even further with the province.
"Our squad retention programme for next season has gone very well. In the last few months, five of our props have signed contract extensions and this is an area in which we are now very strong going into next season."
"There are still a number of areas we are working on and, over the coming months, we hope to announce additional player recruitments as we seek to build the strongest squad possible."
Both players can play at loosehead and tighthead.