Here are two examples from the Forgotten Realms, with clear in-game stories explaining the cause of the changes:
Mystra, the goddess of magic, has had multiple incarnations. In her initial incarnation, she was called Mystryl and was CN. After her first "death" due to the folly of a mortal mage (Karsus), she reincarnated herself as Mystra and became LN. While Mystryl was about the endless possibilities of magic, Mystra was about structure and maintaining order. Later, during the Time of Troubles, she got reincarnated again as Midnight/Mystra and turned NG. While earlier Mystra was not interested in what purpose magic was used, Midnight encouraged its use to make Faerun a better place. (The fourth incarnation is still NG.)
Amaunator, the solar deity of law and order, used to be LN. After losing too many worshippers, he died (or became dormant). When he got reincarnated centuries later, he was briefly LG (4th edition), as his followers believed that he had merged with/he was also the God of Dawn, Lathander (a NG deity). Following the event known as the Second Sundering, he came back to his old self, separated from Lathander and turned LN again (5th edition).
Here are two more examples, but without any specific and well-established in-game explanations:
Tempus, the god of war, used to be CN in all editions of the game before the 4th. During the 4e, he became unaligned (as the alignment system was simplified). Strangely, when the 5e brought back the original alignment system, he became N, not CN. We can speculate that the formalization of a code of conduct called "Tempus's Honor" amongst his followers is relevant; perhaps Tempus started to care more about something like real-life Geneva Conventions.
Siamorphe, the demigoddess of nobility, was LN in all editions of the game until the 4th, during which she became LG. She is not listed amongst the deities of the Faerunian pantheon in the 5e Sword Coast Adventurer's Guide (SCAG), so we do not know what her alignment is now. However in SCAG, it is now stated the s/he is incarnated as a different noble mortal in each generation, so we could take this as the retconned reason for the change in her/his alignment.
If you want more details, there are a lot of FR sourcebooks, as well as nicely written summaries on the web.