Legal deer hunting rifles are chambered for the following calibers: .357 Magnum, .357 Maximum, .38 Special, .375 Super Magnum, .375 Winchester, .38-55, .41 Long Colt, .41 Magnum, .44 Special, .44 Magnum, .444 Marlin, .45 ACP, .45 Colt, .45 Long Colt, .45 Winchester Magnum, .45 Smith & Wesson, .454 Casull, .460 Smith & Wesson, .45-70, .45-90, .45-110, .475 Linebaugh, .50-70, .50-90, .50-100, .50-110 and .500 Smith & Wesson.
Its a shame they left out the 405 Winchester and 450 Marlin. Sounds like the 375 Win or 444 Marlin would both work quite well.