Electoral College

Could a state legislature appoint its own electors after an election has taken place?

No, the Electoral Count Act 1887 prohibits a state from changing the method of selecting electors after election day.

https://static1.squarespace.com/static/5e70e52c7c72720ed714313f/t/5f625c790cef066e940ea42d/1600281722253/State_Legislature_Paper.pdf