I have had stained travertine before. I think it was done with a glaze as opposed to a wood stain. (I would personally not use wood stain.) It made the tile (and grout) darker. It still looked like crappy travertine, just darker. Is that the look you are going for?

Is this travertine on the floor?

yes - after doing more research with the previous owner I now know its slate. Thinking about a concrete stain...

Does your floor look any of these laundry rooms? Find it hard to believe that the floor is just in the one room. Floors like these are usually used throughout a floor. Slate is a pretty classic floor. I would not try to paint or stain it.

I have never heard of someone staining slate .. or travertine .. but then again I wouldn't think it's ever a good idea to paint tile floor or a laminate counter top. It's all just short term lipstick that these DIY bloggers hit you with as good ideas.

If you want to test it out; buy a similar piece at Home Depot (or wherever you can find one) and stain that one and see how it looks. The grout is another story, you will have to pull out the existing grout, say with a Dremel type tool until you get to a depth that when you re-grout it it would settle and stay put -- at least an 1/8-1/4". But, if you are restaining then this could be tricky as to what you do first. Remove the grout, restain, re-grout?? Then the stain may wipe away when the sandiness of grout rubs along it?? I'd live with it until I could afford to replace it. Find another area of the house to put in the time/effort and money into for now.

Slate is a gorgeous upscale natural material. What do you not like about it?

Natural stone is porous and will absorb stain. If you're planning to stain the tile, stain the grout too. Do not worry about removing and redoing the grout, too much of a headache in the long haul.
Do not paint. Over time some moisture may come entrapped between the slab and paint causing the paint to peel up over time. Normal traffic (walking) in the room will also cause the paint to peel over time.

There are always tricks to the trade.

If you just bought the house, try living with the laundry room tile as is for a few months. Then buy a couple sample tiles at Home Depot and experiment. Grout Renew can work in situations where there is little wear and tear or where the homeowner can easily reapply it.

Since we now do not know what you have maybe a couple of pictures of the floor would help but IMO staining stone will not be a good idea

No. Have it covered with rugs.

I would appreciate advice on staining a travertine patio. It was supposed to be a golden color and instead, it's cream. I am told wood stain works. Anyone?? Thank you.

Has anyone every painted over travertine tile to make it lighter? It's a beige/orangey color right now. I'd like to make it white. Can it be done?

I have the same problem with a travertine floor in a kitchen,entry, family room anddining room area. It appears dingy with dirt trapped in the crevices that I have not been able to remove. Would love it to be a charcoal grey. I tried some concrete stain on a sample as I hear its porous, but not so. It looked worse than before. The stain just sat on the surface. I did superclean the sample first too. I would say if you want it white, be prepared to paint it, knowing what you use will only be sitting on the surface so any scratches will show what is underneath. I havent given up yet though. Definitely get a sample to play with first.

Is it possible to paint or stain travertine tile in a shower stall?

I wouldn’t, but if you are dead set, I would prime with sw extreme bond and epoxy paint

Travertine does stain, try wood stain

I am removing some grey epoxy grout from my brown travertine tiles. A tiler named Roman started grouting my new travertine tiles with grey grout instead of brown that we both agreed on. So weird. Anyway, I am removing it and I have a new tiler. So I have a few scratches from my grout removal nightmare but I am happy to report that my medium brown wood stain covers them up great!!! They are not deep otherwise I would be looking for other ideas.