An option is powdered analine dye. You can mix it in warm water, then strain it through a coffee filter into a jar. To apply, put it into a old spray bottle like a Mr. Clean spray bottle, spray it on and wipe it off right away.
The good thing about analine dye is, each time you apply it the color gets deeper, which is not the case with regular stain. Test on a large piece of scrap before using.
You can order it through a supply business like Woodworkers Supply.

"Green" in the finishing palette is "raw umber." Unless you go to a specialty store who can custom mix stains from UTCs or a commercial products distributor, you will need to hunt around because you are unlikely to find a can of something called raw umber. Depending upon the brand, it could be about anything -- fruitwood, light pecan, provincial, etc.

I would also advise against tung oil.
- It provides virtually no protection against water
- It is two to three times as expensive as ordinary boiled linseed oil, and even experts would be hard pressed to tell the difference side by side.
- If you don't do it exactly right (sufficient drying and sanding between) you end up with white spots. The only cure for this is stripping and restarting
- Many products out there are called Tung Oil Finish and the only tung oil in it is on the label. They are typically highly thinned varnishes or varnish-linseed oil blends

Here is a link that might be useful: raw umber swatch

You can get green in analine dye. I use it many times for just the reason you specify. Green kills red. You can order it from most woodworking catalogs.