You are probably going to have to start mixing.

If you want a good finish job stripping to bare wood is going to give the best results.

Depending on the 'look' you are after pigment stains, aniline dye, or some combination of the two may be required.

Using gel stains as a glaze (which is what you would be doing by applying it over the existing finish) can shift the hue or darkness a notch or two before it starts to look like paint. You don't say what the existing color of the oak is, but like brickeyee, I think you'd get better results with stripping down to bare wood. Do this with a chemical stripper, not a sander. Trust me on this one, you will get very tired of sanding and buying more sandpaper and disappointed with the results when the stain does not go on evenly.

There's no good way to tell you what color stain to use because each manufacturer's finish chemists have a different idea of what "Provincial," "Dark Cherry," or "Red Mahogany" mean to them. And the guides won't be any good because each wood, and sometimes each piece of wood, might take a stain differently.

I would just avoid consumer-grade stains such as the M-word. Go to a good paint store or woodworking supply store.

I just refinished the top on a water-damaged end table, without having to do the bottom. It took spray stain (two coats of reddish brown), wiping stain(espresso), shellac (blond) sealer coats, two clear top coats, glaze (Van Dyke Brown), more top coat, toner (walnut), more top coat. So doing a finish to match is more like sailing a boat than it is shooting a rifle. You don't just go pick up a can of #432 and expect it to be a great match to something else.

In other words, test before committing and know how to adjust mid-stream.

You can use Mohawk Ultra Classic Toner, Red Mahogany aerosol spray, to change the tone of the red oak to the color of Brazilan Cherry, such as it is. It will look like Red Oak stained to the color of Brazilan Cherry. The main thing is, to get a large piece of Red Oak, finish it with a clear finish, let it dry for a few days, and then practice with the toner. Stand about four feet away and let the mist float down. Follow directions on the can.

I don't see the economy in staining an existing Oak railing to match new Jatoba floors. I don't think you will get results you are pleased with, and considering the money spent on floors, why not do the railings too or else leave it alone for another time.

Or consider painting the Oak a solid color. The oak grain pattern will show through and the solid pigment can be an accent to the other interior colors.

Thanks everyone for taking the time to respond.

I have started stripping the banister and sanding it. I will try out the various stains on a red oak as suggested and go from there. if I really can't match something close to cherry. I am thinking I will try a dark color like dark brown stain. I went to wood working store and got a a couple of stains from general finshes today. If all else fails I will just paint it ( my husband won't be happy if I did this).
I will let you know how this goes.