"A form of coke sold as a smokeless fuel, especially for heating", Early 20th cent.; earliest use found in The Trade Marks Journal. From coal + -ite.[Coalite etymology, Coalite origin, 英语词源]
"And without object To combine, unite, merge; specifically to form into a coalition", Late 16th cent. From classical Latin coalit-, past participial stem of coalēscerecoalesce. In later use perhaps partly after coalition.