Bob,
The play can be either in the bucket pins and bushings, which is impossible to fix without replacing them, or the cylinders aren't full of fluid.
The second situation seems like an answer a nutcase might put forth, but humor me on this. Grab the bottom edge of the bucket and try to tilt it up while you watch the dump cylinders. If they compress slightly, you have what's called a "floppy bucket". The fact that it has a name (I didn't just invent it, really) tells you how common this is.
What happens is this: when you dump a load of heavy material out of the bucket, the hydraulic pump can't keep up with the cylinder travel (they are "driven" by the load in the bucket), and air gets introduced into the dump cylinders. Where it comes from is another question, and a hot one I don't want to get into.
If they do move slightly when you lift up the bucket lip, try this: start the tractor and hold the joystick in the full dump position for about 5 seconds after you hear the relief valve open on the hydraulic pump. It usually takes about 5-10 seconds. Do the same in the full curl position. When you're done, level the bucket and try moving it by hand again. I'm willing to bet it'll be pretty solid unless your pins are worn.
What you're doing is getting any air out of the cylinders and replacing it with fluid, which is nearly incompressible.
That's the good news, the bad news is every time you dump a heavy bucket full of material it'll cause the same thing. It's not harmful unless you need exact control over the bucket for some job.
Sean