The Collaborative International Dictionary of English v.0.48:

Beseechment \Be*seech"ment\, n.
   The act of beseeching or entreating earnestly. [R.]
   --Goodwin.
   [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

47 Moby Thesaurus words for "beseechment":
   Angelus, Ave, Ave Maria, Hail Mary, Kyrie Eleison, Paternoster,
   adjuration, aid prayer, appeal, beadroll, beads, bid,
   bidding prayer, breviary, call, chaplet, clamor, collect,
   communion, contemplation, cry, devotions, entreaty, grace,
   impetration, imploration, imploring, imprecation, intercession,
   invocation, invocatory plea, litany, meditation, obsecration,
   obtestation, orison, petition, plea, prayer, prayer wheel,
   rogation, rosary, silent prayer, suit, supplication, thanks,
   thanksgiving