It is particularly important to note how Capote uses these references to develop and build the particularly complex character of Perry Smith. These three symbols that are used again and again clearly indicate the way in which Perry Smith is a character who is conflict with himself and a composite mixture of odd parts. On the one hand, there is his physical condition, with his weakened legs incongruously supporting his powerful and muscular torso and shoulders. He is in constant pain because of the motorcycle accident that left his legs so weak, and chews asprin to try and control that pain. The numerous references to "bubbles in his blood" when he is scared or angry seems to refer to his unhealthy condition and the way that he is dominated to such an extent by his emotions.
The symbols of the coyote carcasses and the avenging angels seems to capture the mixture of maturity and immaturity in his character. On the one hand, he is clearly a sensitive and intelligent individual who could have gone far if he had been able to continue schooling. He is a self-taught painter and musician and he shows great academic potential. However, on the other hand, he seems trapped in a childlike state. He continues to wet his bed, he sucks his thumb and he cries out for his father in his sleep. The influence of his Irish, Catholic upbringing is shown through the many care homes he stayed in as a child and the symbol of the avenging angel.
The three symbols you have indicated are therefore used to point towards the complex nature of Perry Smith's character and the strange mix of different parts that he represents.