Do you have a special tinting dye or process that doesn't cost too much? 

For these chairs, I used Mohawk brand lacquer and tinted lacquer.  For large pieces, they sell concentrated dyes for mixing with the lacquer to whatever tint you want but for these chairs I just used their rattle cans of tinted lacquer. They sell pre-blended colors like dark walnut or the base colors which you can mix to get literally any color you want.  With the rattle cans, I could experiment with different tints and layer them without a huge investment in a bunch of concentrated dyes.  IIRC, each can was about $8 and I use between 2-3 cans of 2 different types of brown. For all 8 chairs and I used about 3/4 of a gallon of lacquer which was under $60.  Spraying lacquer wastes a lot of lacquer.  Probably half of it is over spray that blows past the chair.

Here is the process I followed:
  1. Spray 2 clear coats on the bare wood.  This seals the wood and prepares for the tinted lacquer.   I used a semi-gloss on these chairs.  This basically prevents the tinted lacquer from staining the wood.  
  2. Lightly sand the seal coat smooth.  If you have better spray equipment and more experience spraying lacquer than I do, this should be minimal. I was able to get mine smooth enough with a quick pass using gray 3M abrasive pads. 
  3. Spray the tinted lacquer over the seal coats,  blending the 2 tints until I got the shade I wanted.  I started with very light coats to sort of dust the surface with the tint and added more until I got close to the density I wanted.  This is how you control the darkness of the color.   The 2 shades I used were Vandike brown and Dark walnut.  I found the Vandike was too green and walnut was too red but blending them got me a color in the middle that matched the table well. In this case, I usually started with the Vandike and used the walnut to move it away from green.  It was actually kind of cool seeing how the color morphed with just a light spray of the second tint. 
  4. Once the color you want is achieved, spray several coats of the clear to seal the tinted coat and get the finish you want.  

One nice thing about using tinted lacquer is that if you do not like the result, you can simply use lacquer thinner to strip it off and try again. 

Note that I used a Color Muse (thanks for that tip, Rich) to check that my eyes were giving me a color that was close to  the target color of the table.  Wood grain is naturally variable so I used the darker grain in the table as a comparison.  After finishing the first chair, these are the results of the comparison.  I think that the table was on the left and the chair on the right.



I actually bought the Sherman-Williams branded version of the Color Muse.  It is exactly the same device and works with  the Color Muse app as well as the Sherman Williams app but was a little cheaper than the Color Muse branded one.  I've used to this to help find paint colors as well.  

--Nathan, TX. Hire the lazy man. He may not do as much work but that's because he will find a better way.