How do I repair two table that have some kind of stain that's peeled?

If the stain just came off and there aren't any gouges, you might try a matching stain pen to color in the spots and wipe off the excess. Or you can very lightly sand the top and apply General Finishes Gel Stain over the existing stain. The top will look like new.

Here is a link to the stain, it is also available locally at certain hardware stores.

https://amzn.to/2NHolbR

You could get a veneer for the top, it’s put on with rubber glue.

That is not stain that is peeling, that is a thin wood veneer that has peeled in areas. You can purchase wood veneer but it takes some know-how to remove the old veneer and then cut and glue the new veneer down. This happens when the finish (laquer, varnish etc.) wears over time in heavily used areas and then the thin veneer dries out or is exposed to humidity which will make it lift and peel. If you look closely you can see where the veneer seams are. I would probably sand the tops and if it is real wood underneath you could try to match the stain that's on the rest of the piece. If that doesn't work paint may be your best choice. Good luck.

Yeah, that's definitely veneer damage. There isn't an "easy fix." I agree with Kal. I don't know that sanding would necessarily work because you'd want to remove all the veneer and that seems it would take a LOT of sanding to try to get that done. Maybe just sanding smooth to the touch, and then try the light test to see if you can spot any areas on the surface that "jump" out at you when you get down to eye level and look the table over across the top. Running your fingers over and over the area lightly will also tell you where you may need to sand a bit more to smooth things out as much as possible. Really give the wood a good go-over after sanding to get rid of all the residue. I used the "old fashioned" tack cloths myself. They have a sticky stuff in them that grabs every bit of sanding residue and wood residue. There are separate things that you should do to prep the wood depending on whether you are going to stain it or paint it. So look around online. There are lots of "how to" step by step instructions websites and videos online.

Try using some furniture refinisher, such as Formby's, then restain and seal. The wood looks to be in ok shape, but you may have to very lightly sand.

Many factory applied finishes are only on the surface, so water has resulted in the finish itself lifting. When you restain, it will actually soak into the wood.

Okay thank you.