Are there some commonly used abbreviations for "gerund", "gerundive" and "supine"?
Two of those are listed on Wikipedia:SUP for supine, (use SUPL for superlative if both terms will be employed in one work) and GER for gerund. Neither is found in the Leipzig Glossing Conventions, which is fast becoming a standard in linguistics. Lehmann (1982) contains a suggestion only for gerund (GER). An undated though recent paper apparently by C. Lehmann suggests OBLG for gerundive with the note ("use obligative").
Looking up the parameter VerbForm in the Index Thomisticus treebank in Universal Dependencies I find Ger for Gerund, Gdv for Gerundive, but a tag for Supinum is missing.The PROIEL treebank has Sup for Supine (for strange reasons, only the Supine in -u is found there).