the problem is one of science, chemistry, physics, whatever... the temperature of the liquid determines, in part, the amount of CO2 saturation. Time takes over next, unless you improvise with shaking or something else. Hope it works.
For what it is worth, I intend to experiment with a diffusion stone on a modified gas in tube for my next keg. I have been told that with the diffusion stone submerged towards the bottom of the keg it will be carbonated in about one day, once it has reached proper temperature. We shall see.