Synonyms for Longing:

adj.

desirous (adjective)
acquisitive, amorous, anxious, ardent, covetous, craving, desirous, eager, expectant, fond, grasping, greedy, hankering, hopeful, hungry, itching, needful, passionate, pining, ravenous, urgent, yearning, Lusting, Thirsting.
hoping (adjective)
wishing.

n.

ache, enthusiastic, ravenous. anxious, appetence, impatient, keen, yen, be dying for something/to do something, in need of something, in the hope that/of. desire (noun)
acquisitiveness, amorousness, covetousness, craving, desire, eagerness, expectation, fondness, greed, hope, hunger, itch, lust, need, passion, thirst, urge, wish, Ardency.
feeling (noun)
yearning.
longing (noun)
yearning.
strong desire (noun)
hankering, hunger, itch, thirst, urge, wish, yen, Hungering, Coveting.

v.

desiring (verb)
pining, wanting, welcoming, wishing, Desiring, Expecting, Fancying, Hoping, Hungering, Needing, Coveting.
lamenting (verb)
agonizing, clamoring, crying, grieving, groaning, lamenting, moaning, mourning, sniffling, snuffling, sobbing, wailing, weeping, whining, Bemoaning, Bewailing, Decrying, Sighing, Ululating, Whimpering.

Other synonyms:

appetence. ache, yen. keen. Other relevant words:
ache, anxious, appetence, enthusiastic, impatient, keen, ravenous, yen.