$300 seriously limits your options. Start browsing used gun stores and looking in the paper.
A lot also depends on how you will be hunting those coyotes. If you are close enough a shotgun or .22mag will do the job. That would save you a bunch of money.
I don't think much of a Nagant as a first rifle. Too much recoil, crude sights and they just aren't that accurate.
You should reconsider getting a single shot such as this
http://gunbroker.com/Auction/ViewIte...Item=138680785
surplus .223 and .308 ammo is available and you can find several rifles chambered for those rounds.