The easiest way would be to use a fingertip to cover the spout opening while pumping the handle to create a siphon suction.
I have a 78 Trill and recently I had the same problem. I would have to suck the end of the tap to get it started, then it would only be good for a short bit before back draining to the tank. The coleman rocker pumps have a metal ball check valve in the bottom of the pump. When I removed the pump last week, the metal ball just fell out becuase it rusted and wore down in diameter.
I replaced it with a nice solid metal rocker pump with a glass marble inside from the local RV shop for $40 and its the bomb