Ok, I've studied Latin in high school but it was a long time ago :-)
"Conentur" is the third-person plural present subjunctive of "conor" (to attempt, try).
"Se invito" is the so-called "ablative absolute" (here using a pronoun plus an adjective). It can be translated as "against his will", or more literally as "he (being) unwilling".
Hope it helps,
tano