Tetrapoda is most often ascribed to Goodrich's (1930) book on comparative vertebrate anatomy, but the name was not introduced as new there, it was used as already known. Having encountered earlier uses, I went on a Google binge [pun not intended] some 5 years ago and found some 19th-century work by Haeckel attributing the name to Aristotle (the legal fiction that taxonomic nomenclature began in 1758 took a while to become entrenched).
Finally, someone has dug through the literature for real and documented the results! The conclusion is: 1) most ICZN rules, including priority, do not apply above the family group of ranks (erroneously called "the family level" in the paper), so ultimately there is no objective way to decide; 2) the closest thing to an explicit use as a new taxonomic name in the modern sense – there are homonyms – is in Jaekel (1909), so that's the best option to cite.
Jaekel, O. 1909. Über die Klassen der Tetrapoden [About the classes of the tetrapods]. Zoologischer Anzeiger 34:193–212.