Good grief, I look at this new-to-me word and my mind wants to jump to "oppossum"! Adversative is a new word for me, too. You've stumped Gurunet with oppositive, but it likes:
ad·ver·sa·tive (ăd-vûr'sə-tĭv)
adj.

Expressing antithesis or opposition: the adversative conjunction but.

n.
A word that expresses antithesis or opposition.

[Latin adversātīvus, from adversātus, past participle of adversārī, to oppose, from adversus, against. See adverse.]
Now I'm wondering: are either of these words ever used to describe anything but 'but'? Are they used for conjunctions only? Couldn't terms like "extra-large shrimp" also be described using either of these words? What if the ex. read poor and happy? Would the and be considered an oppositive/adversative?