I have one just like that one, and know of a couple of others, all with 20 inch barrels. Yours looks shorter. On another website, straightgripped Marlins are often described as "Texans". I wonder, though--since every "Texan" depicted in submitted photos seems to have a lever which is not rounded like yours, mine, and others that I have seen, but is squared off at the back. Having grown up in Vermont (before the gentrified, liberal flatlanders overran the place) leverguns were the norm for the locals who you'd see out there deer hunting. Winchesters and Marlins were the most common. Until I moved to Northern Vermont in the Mid-80's I had never seen one configured quite like the one in your picture, or the one I bought (used), or the well-worn ones owned by a couple of locals up here. I had seen the some of the "Texan" styled ones before, but not many. The common Marlins had pistol grips and big, fat, ugly fore-ends.
One of the stocks that are cut for the current straight-grip Marlins ought to work--you'd need to find one that doesn't have that checkering that Marlin likes to uglify their latest models with. Try Precision or Treebone. Both have websites and would be a good place to start.