The pigments in paint are much different than in stain. Latex and oil based paints use clay while stain is simply chemicals. You can thin latex with water and try and find a small strip to test it on, thinning until you get the look you want, but if it were me, I get some deck wash and a garden sprayer, spray it one and power wash or really hose it off. You'd be surprised how well an old fence comes to life when the deck and grime are off plus the deck wash has a bleaching agent in it to support a new weathered look. Next year just use some exterior polyurethane, buy a small paint sprayer and spray the fence to seal it in. I have two hundred feet of fencing and round one was less than $100. I'll let you know what the urethane is going to cost but it should be about the same.
