Most antelope hunters I've met hunt with a bolt action rifle in 270. My best friend hunts with either of his Rugers in 220 Swift or 25-06. Both are lethal long range antelope cartridges.
Pronghorned antelope are not big animals. Avereage mature doe weighs about 85 to 100 lbs. A really big buck is rarely heavier than 115 lbs or so. Their hides are thin compared to elk or moose. Very large lungs with oversized heart and major blood vessels are found inside the chest. This is why they can run so fast! Yet a hit anywhere in the chest will quickly topple the animal.
This kid/buck weighed about 80 lbs and was dropped in his tracks at about 275 yards or so. A chest hit that destroyed the lungs. Rifle is a Remington slide action in .243 which is unaltered. It left the factory as a tack driver! I've used a variety of bullets over the years. 80 grain Sierra Pro Hunter, 85 grain Speer, and others. But best accurasy for me has been with 95 grain Nosler Ballistic Tip.
Good hunting to you.