Search rambler engine swap. The 196 OHV will bolt in where the L-head was -- they are virtually the same engine from the head down (some casting differences on the valve side just above the side covers, can't convert the L-head block to an OHV head).
There are only a couple engines that easily fit the narrow and short engine bay (mostly narrow!). The small Ford sixes (144/170/200/250) will JUST fit. You will need the transmission along with the engine. The 200 and the 196 OHV have about the same power, the 250 a little more and is the newest of the bunch. If you have to look for one, get a 250! The 250 will also bolt to a SBF transmission. For more on those go to www.fordsix.com
The best modern engine would be a 2.3L or 2.5L from a Ford Ranger. Has to be EFI with the intake that curves over the valve cover. It will just squeeze in. Not too hard if you get a donor truck and just swap everything over. The rear axle is a bit wide, but with deep offset wheels you can make it work. Swap the entire dash in for a real cool project, but don't try setting the Rambler on the Ranger frame -- not unless you cut the floor out and drop it over the rails. That's more work and expense than rebuilding the Rambler front end -- which will easily handle the weight of a small block V-8 (the old L-head six is 550 pounds!).
The Quad Four fits due to the front driver intake that curves over the valve cover. The big expense is the trans adapter or bell housing. Around $500 for that one piece, and it's a must have to convert the motor to rear drive.
Other front driver engines with intakes that curve over the valve cover might fit, but converting to rear drive is an issue, and all would be EFI.