If you mean the fur on the belly turns reddish, one cause is chronic licking due to itchiness. Dogs with allergies who lick their paws or front legs will cause the hairs to turn reddish brown due to the porphyrins in their saliva that stain the hair a reddish brown. Not to be gross, but if you could look at a gallon of dog saliva it would resemble dilute iced tea. If you painted coat after coat of it onto a white wall eventually it would turn a reddish brown as does the fur on a licking dog. I would expect the same is true for coyotes.
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