Google up Hogzilla lights or XLR 250 (I think I got that number right). I got 3 of them and they clamp to a scope very easily. In the case that you are using open sights, the clamp should fit the magazine tube. I got the red light version, but they offer a green version also. I can't tell you what maximum range is, but I can (and have) shot coons at 135 yards and could see the coon quite clearly. The red light doesn't seem to spook coons or coyotes, but I can't speak for deer and hogs (not yet anyway).
I have one light on my Marlin 39A (clamped to the barrel and mag tube) and two on centerfire rifles - clamped to the scope.
You can also go to Lightmalls.com and buy them direct from China, but it wasn't easy to navigate on that website. The lights are much cheaper if you do it that way ($27 each). You'll need an extra battery or two and a charger and the clamp is a separate item also. That's the website where I got all my gear. Shipping time was about 2 weeks or so, if I remember correctly.
Can't you just put a small rail on the forend?
mitranoc, I could be wrong, but I think that the HZ and the XLR are exactly the same light with different names from different folks selling them. That's why I went direct to Lightmalls.com. Took me a while to figure out the website and find all of the stuff (lights, mounts, batteries, clamps) and order it, but for $157 shipped, I got what I needed at a third of the price of buying HZ or XLR. What I bought from Lightmalls was the Ultrafire 802 (I think). Anyway, if you buy a couple of them you might want a green and a red. The green supposedly has more range because it's brighter, but I'm perfectly happy with the red. And with the red, for some reason that I can't explain, the eyes of the coons (for instance) are super bright, which makes them much easier to find in the trees in the pitch dark.
Prior to the Ultrafire, I had a midpriced light from Primos, with a heavy battery. I can't adequately express how much better this setup is. I definitely got my money's worth.
With the larger diameter mag tube on the Marlin 336, the clamp will probably work best just on the mag tube.
I wonder if that's to reduce reflection off the front sight.
Unless you're in a hurry, order the light and the basic screw-type clamp and see if it works on the mag tube or scope. If not, spend the money on the fancy mount.
If you are anywhere near central Texas, come on over and try my light on your rifle. And have a beer.
why use all that money. a couple of zip ties will solve the prolem.