I'm no expert, but here's what I did
Well, it isn't a Marlin, but it has a laminated stock and i pretty much did just what you seem to be wanting to do.
So, I got this Feinwerkbau 601 RT, which is perfectly good function-wise, but the stock was in a very sad condition. Also it was ugly for my eye even if it was in mint condition. So, I decided I have pretty much nothing to lose.
I had never worked on a laminated stock before. Or any stock. And very little with wood in general... Anyway, I went on.
First I sanded off the chipped 30-odd old laquer with a small and pointy vibrating electric sander. I then proceeded to fine 220-grit sandpaper. Once I had that done, I had a nice, bare piece of furniture..
I then aqcuired some solvent-based stain (mahogany color-you can go darker by adding but it's difficult to get lighter) and applied generously with a paintbrush. Then immediately took a piece os 220-grit sandpaper and sanded the wet stain into the stock thus avoiding uneven staining.I wiped off the excess stain and repeated the procedure, forcing the stain into the stock, it took many repetitions because the laminate resists absorbing, but finally I reached the desired tone. I let it dry overnight and then gave it a light sanding and wiped off the dust. The result was just about the colour I wanted, but very dull and almost like a burned look.
Thought for a while if I should beewax it, but then decided to use cooked linoil (varnish). The first layers I laid with a combilation of varnish and (pine) turpentine, the dullness was immediately gone and the stock had a nice semi-matte sheen. I could have stopped there and just polished it a little, but instead I applied more varnish, this time thick and without any added turpentine, just smeared it generously all over the stock with a rag, applying some pressure, let it sit for a while, wiped off the excess linoil and repeated until I had a deep satin glow, the grains and layers forming nice patterns that could have been accentuated even more by continuing with the varnish or adding clear laqcuer, but I decided to stop there because that was just what I wanted.
If this iPad cooperates with me, I will edit and add some pictures. If it doesn't, I hope you catched the drill. Overall this operation took about three hours plus the night the stock dried after the staining.