The story
From the Latin name for Melbourne, Melburnia, + -ian. The term can be traced back to 1876, when the case for Melburnian over Melbournian was made in the Melbourne Grammar School publication, the Melburnian. 'The diphthong, ‘ou’ is not a Latin diphthong: hence, we argued this way, Melburnia would be [the] Latin form of name, and from it comes Melburnian.'
Etymology from Wiktionary, CC BY-SA 4.0.