Synonyms for Tranquilize:

n.

reassure, talk down, put/set someone's mind at ease/at rest, comfort, put someone at (their) ease. balm. tranquilize (noun)
lull, still, calm, tranquillise, sedate, tranquillize, quiet, quieten, calm down.

v.

bore (verb)
annoy, tire, bore, fatigue, weary, dull.
calm (verb)
assuage, quell, allay, sedate, placate, still, console, lull, appease.
make calm, quiet (verb)
hush, calm down, lull, sedate, subdue, still, quiet, balm, relax, calm, quieten, soothe, compose, quell, pacify.
moderate (verb)
soothe, restrain, alleviate, compose, ease, soften, calm, quiet, relax, pacify, subdue, moderate, cool, abate.
pacify (verb)
ebb, relieve, conciliate, smooth, reconcile, stabilize, hush, mollify, defuse.
rest (verb)
settle, pause, settle down, subside, mark time, wait, stagnate, becalm, stay, fix, stand, vegetate, rest, slumber, sleep.

Other synonyms:

reassure. comfort. balm, talk down. calm
quieten.
soothe
soothe.
Other relevant words:
comfort, tranquillise, balm, reassure, tranquillize, quieten, calm down.