Melibean is an old literary adjective for something associated with Meliboeus, the shepherd in Virgil's first Eclogue. In poetry, it usually points to a pastoral or bucolic setting, or more narrowly to a Virgilian shepherd's voice and the kind of rustic dialogue found in such verse.
The word is rare today, so it is mostly encountered in historical criticism rather than in modern poetic practice.
Example
Beneath the poplar shade, the Melibean shepherd
counts his flock and answers the hill with song.