RE: What " carry" rifle/caliber for rabbits and coyotes?
You are going to have a very hard time trying to find an ideal rifle to use for both of those two animals. If you were to choose a rifle for each seperately, I would see a .22 rimfire and a .22 centerfire such as a .223 or .22-250. So if you ask me I would comprimise between the two (considering you will be shooting an equal amount of each animal) and go with a .22 Hornet. You didn' t really talk about your budget but if you go with a Hornet, an NEF single shot would be the cheapest way to get things done. If you want a bolt action, you could buy a classic CZ American or a super slick Browning Micro Hunter. If you want a wonderfully designed American beauty, you can buy a Ruger #1 and if you want to be different, you could go with a Taurus Raging Hornet and have the ultimate in totability.
You more than surely have a few caliber choices but I feel that a Hornet would be your best comprimise between true small game finesse and varmint power.
Josh