That looks very similar to mine, but I'll have to check what brand mine is tomorrow.
I don't change the water daily. I do usually go pour out what's in the tray each day, swish it around a little bit, & let it refill with fresh water.
I take the bottom off about once a week or so (sometimes I do it less often) & clean & scrub the whole thing with Dawn, rinse it real good. Then, I soak it in bleach water to disinfect it. Then, I rinse it real good, put it back together, put the little screw on cap down on the little port hole to prevent it from leaking while I fill it, fill it up, put the lid on real good to prevent it from leaking when I remove the little cap. Then, I set it down on like 3 of those concrete patio squares, take the little screw-on lid off the port & put it back where it goes & water comes out the port & only fills up maybe the level of the hole. (I always know I didn't put the lid on tight if the water fills all the way up).
The reason I'm saying all this that you probably already know is because when I first got the waterer, I couldn't figure out how to keep from wasting water with it flowing out the tray/trough...trying to hurry up so I could hurry up & put the lid on to keep it from leaking. Then, I figured out that's what the little screw-on cap was for....LOL.
. If that ain't bad enough, I have also forgotten to remove the little screw-on lid from the port, therefore, the chickens couldn't get any water!
. Luckily, I only made that mistake once & it was only for a few minutes....learned my lesson from that!
Anyway, what about taking the tray off the old one & using the new tray (if it fits) & see if it still leaks. Then, you will know it's the tray. But it sounds like it may have some sort of small crack in the tray that could probably be sealed & fixed.