Are traditional hunting semiauto rifles an option?  If so,

Remington 742 hunting rifles (and other variants) are available in .243, 244 (6mm Rem), .280 Rem, .308 Win, .30-06
Browning hunting BAR in .243, .270, .308, .30-06, 7mm Rem Mag. .300 Win Mag

These come to mind.  While they are magazine fed, the OEM magazines usually limit capacity to 3-4-5 shots depending on calibre.

Larger capacity magazines may be available from aftermarket sources.  These are powerful hunting cartridges and the civilian hunting BAR is available in magnum loads including 300 Win Mag.

Unless you anticipate a need for high magazine capacity (if legal) they perform extremely reliably if sustained fire is not needed.

Fair point.  There were the semi-auto Winchesters in .243 & .308 as well.

The M1 Carbine is banned by name in NJ, if I recall correctly.

Geez.  Any links?

It's kind of obscure, but one of my grail guns is a Remington model 81 in 35 remington with the Kreiger 15 round detachable magazines. I can't imagine a Remington model 8 or 81 being banned anywhere. The standard models with internal magazines aren't even that much money, especially for the less desirable cartridges.