Natural cane is light colored and may not create the look you want for your cane back or cane seated chairs. Because natural cane is a hardy species that is not very porous, it doesn't take stain well. To achieve the darker stain look that you want is likely to require several staining experiments to achieve. It may also be beneficial to pre-stain your cane prior to installing it in your chairs. In this way you can achieve a more uniform staining appearance, and you may only need to do some small touchups after the cane is installed.
Stain and finish the frame of your chair to the color you prefer. Use this chair as a base of reference for test staining your cane.
Pour the same color stain that was used on the chair into a shallow pan (a disposable pie plate will work).
Wearing gloves, immerse a scrap of cane into the pan. Because cane has a natural hard finish that tends to repel staining, the stain may not absorb well. Time the immersion, and allow test pieces to dry after being submerged for different periods of time. The splines of the cane will darken faster than the rest of the cane. Remove the test pieces from the stain bath, and allow each test piece to dry 10 to 12 hours.
Rub a rag across the test pieces to see how much of the staining lifts.
Compare the test cane to the chair frame. If one of the test pieces achieves the depth of color you want, use a larger pan (like a restaurant-size baking sheet) and immerse cane that is large enough to fit the chair. Remove at the correct time, and allow the cane to dry thoroughly. Rub residual stain off.
Install the cane into the chair frame.
Apply artist oil paints to test pieces of the cane to darken the cane. Rub or brush the paint on to achieve the look you want. This paint will tend to harden on the surface of the cane and will be subject to wearing off as the chair is used.
Lightly mist (a different stained test piece of cane) using a tinted lacquer spray paint. Lacquer will also wear off easily. Compare the different test pieces to see which achieves the look closest to what you want.
Install the stained (and painted) cane into the chair after it has dried at least 24 hours. (Oil paint may take several days to dry.)Touch up any spots on the cane. Mask off the wood frame and spray 3 to 4 coats of satin finish clear to seal the paints and stains to the cane for the longest wear possible.