Coyotes mostly feed on mice, voles, and rabbits. They could kill a raccoon (particularly young ones). But an adult raccoon (up to 27 pounds) can weigh almost as much as a coyote (most 20 to 40 pounds, occasionally up to 55 pounds), and they put up quite a fight. Most coyotes would not take the risk of going after an adult raccoon. But with wildlife, you learn never say never.
In addition to not feeding the birds, make sure pet food is not left outside, keep grills clean, and trash should be stored securely (it attracts mice, which attracts coyotes).
My guess is that the raccoons going crazy in the tree had more to do with breeding season than seeing a coyote go by. Raccoons breed January through March, and a female will mate with several males.