When facing tuning problems, the last thing you want to look at is your tuners. Don't blame the tuners when your guitar goes out of tune easily. Its very likely due to friction points on the guitar.
The first step I'd take is rub some pencil lead unto the nut slots and the under side of the string tree for extra lubrication. If that doesn't work, your nut probably isn't cut properly. A well cut nut that doesn't bind the string really helps improve tuning. Get a tech to slot the nut properly. Nut material like graphite also are more slippery and lets the string pass through with less friction. Try Graphtech.
On my MIM fender I solved all tuning issues simply by removing the string tree. I can divebomb like mad and I still won't go out of tune even with the stock tuning heads. But I did lose out abit on tone and sustain due to the poor break angle and the nut. Staggered tuners will solve that problem.