If your plan is to do a transparent green, you can do it by mixing green dye or green pigment in the compatible clearcoat of your choice (a tinted clearcoat is called a "toner" in the wood finishing industry). Alternatively, you can mix up a stain with the pigment using a vehicle of 50/50 lacquer reducer and lacquer retarder. The retarder keeps it from flashing off instantaneously, gives you a little more working time and reduces the likelihood of blotching. NB: Dyes do not make for a good stain on darker wood like mahogany or limba.
If you want an opaque green, you'll just use a lot more pigment in the lacquer or what-have-you. You can also start with other shades of green pigment (Mixol offers several, go to their website or to Woodcraft for a color chart) and doctor with black, white, or other shades to get it where you want it.
The Mixol grass green no. 13 in a stain is what I used on the telecaster below. Transtint (marketed as Colortone via Stewart Macdonald) is darker and leans a little more blue. Both are compatible with nitrocellulose lacquer. I don't recall about the dye, but the Mixol pigment is a universal tint, so it is also compatible with other oil- and water-borne finishes. As always, test your finishing schedule on scrap before you start inflicting your will on your actual workpiece.
For a stain color coat, I would use the following schedule:
Sand to taste (220 might be enough, 320 is also fine, any more than that leaves too little "tooth" for the finish to take hold)
Apply stain
Seal with unwaxed shellac (I use Zinsser Bullseye from a rattle-can) or a wash coat of lacquer
Fill grain (the specimen below was filled with water-based Timbermate neutral, tinted with Mixol black no. 1)
Repeat grain fill/sanding until you are ready to throw it out the window
Probably one more round of grain fill
Seal once more with shellac or lacquer
Pile on the lacquer clear coats.
Let it cure a couple weeks
Wet sand
Buff/Polish
Assemble
Summon the lightning from the heavens with your new implement of doom
Notes on the above process:
I was a little stingy with the clear coats on this axe, and I regret it. It's thin, which some of the snake oil salesmen will tell you allows the wood to 'breathe' and 'improves your tone,' but that is arrant bullsh1t, and I really would have preferred a little better protection. But this was an early effort by yours truly, and one lives and learns, hopefully.
But I digress.
The schedule I would use for a tinted lacquer color coat is:
Sand
Seal with unwaxed shellac or lacquer
Sand
Fill grain
Shellac or lacquer again
Scuff sand
Color coat
Repeat color as necessary to get desired intensity
Top coat with clear lacquer ad nauseam
let it hang a couple weeks in a dust-free environment
Wet sand
Buff/polish
Assemble
Rock out