Top choice: AR-10 Anything that works, free floated barrel and flat top upper. A variable hunting scope is required here. BUISs really aren't what this rifle is for. ETA: If it was me, I would also want a suppressor
An AR-10 is going to give you your best value for what you want to do. Semi auto fire is preferable here. When culling hogs, they will usually come in groups, so make the most of each opportunity to fire. Not to mention coyotes are damned smart, so if you miss the first shot, it makes sense to have a quick followup available.
Second choice: SIG 716 A glorified AR-10, that costs more.
Third choice: SCAR 17 A marked upgrade over an AR-10, but for the price, you could also have an optic and a suppressor as well. So... No.
Fourth choices: M1A and FAL Tied. Fun, yes. Efficient, no. More class and 'cool factor' than an AR-10, but at the cost of magazine price and ease of mounting an optic. Iron sighted MBRs were outdated in the '50s...
Dead last: The bolt guns I love a good Mauser as much as anyone, but what you are looking for is not for hunting - it is for killing. Either four legged or two legged predators. Semi auto is best here.