Can you not queue for League Conquest as a party?

No. '-'

You can't, solo only

League ranking is of personal score, therefor playing as a group is not allowed as this would skew your results, give an advantage to you or your enemy being teamed with people they know, play better with, better communicate and synergize with, etc. If there is ever a Duo queue, it would almost certainly rely on a new and separate ELO system.