The Wyandot Indians have an origin myth for sun showers.
Then the Thunder spoke again to the young woman and said, "I have now taken him along with me, and whenever it rains while the sun is shining, the people shall think and say that Tsi-ju'Q-Q, the Wyandot, is making the rain."
Snopes has an array of sun shower folklore references.
Various cultures ascribe the occurrence of these wettings to the marriage of animals, such as rats (Arabic), tigers (Korea), monkeys (Zulu), jackals (South Africa), hyenas (Kenya), or bears (Bulgaria). However, the critters most commonly pointed to are foxes — cultures in numerous spots around the world pronounce a sun shower as a sign the foxes are getting hitched.
The devil is pointed to as the cause primarily in Anglo-Saxon cultures. Says one 1888 book of American lore: “A sun shower is caused by the devil whipping his wife, the raindrops presumably being her tears.” Such explanation is typically phrased in a number of ways (such as “Satan is beating his grandmother”), often with the added detail that the female relative he’s victimizing failed to prepare a particular foodstuff to his liking. Alternatively, the devil may be said to be engaging in a rather undevilish behavior, such as kissing his wife. This latter version serves to provide an answer for the contradiction that is a sun shower; that something which violates the law of the universe (i.e., the devil’s behaving nicely) causes something else which goes against the law of nature (e.g., rain falling from the sky while the sun is shining). Similarly, this odd weather phenomenon is sometimes said to be caused by the devil and his wife fighting, accompanied by the additional suggestion that if one were to stick a pin into the ground and place his ear to it, he’d hear the argument.
Witches get brought into the fray by claims that it’s their churning butter or combing their hair which causes sun showers. Alternatively, in an echo of the “animal” rumor, they may be said to be getting married.