If he's just buying junker engines, it's going to keep popping the headgasket. I can't believe he's done 3 swaps without just putting in the revised multi-layered-steel (MLS) headgasket. Unless the car has been run chronically with a blown headgasket, to the point that the top deck of the block and the head have eroded around the failure point, the MLS if properly replaced is a once-and-donce item. Don't go to NAPA or someplce like that - get the real MLS gasket kit over the parts counter at the dealer. It should be a permanent fix, and it's not all that hard.
If he's set on a junker, find a '99 model year Neon with a build date after about November of '98. That's when the MLS gasket hit the production stream, and they rarely have HG problems.
In answer to your other question, no there's no other block before about that time that is more immune to the problem, because the 2.0 SOHC and DOHC use a common short block, and the 2.4 DOHC uses the same block except with 1" higher deck and consequently 1" longer stroke. In fact the 2.4 DOHC and 2.0 DOHC use exactly the same head. But again, the MLS gasket will cure the problem.
If he wants to swap for fun, the 2.4 DOHC from any of the '95-'99 Cloud Cars (Stratus, Cirrus, Breeze) will fit in a Neon if it has the bulge hood. You can also use an early PT engine, which in fact has a better head than the older Clouds. The swap requires modifications to the engine mounts, and some tinkering with the ignition and fuel injection, but it works fine and it makes a hell of a daily driver.
I did my wife's '95 Neon that way in about 2000, and she drove it (and loved it) for 4 more years before it was drowned in a flash flood. If he's interested, I can talk him through it. It's not hard if you know somebody who can do some minor welding.