Synonyms for Cough up:

n.

allow, come clean, grant, concede, confess, own, admit, let on, profess, acknowledge. disburse, put up, pay out, bear the cost/expense etc., pay, fund, invest in, spend, finance. cough up (noun)
spit out, cough out, pony up, spit up, expectorate.

v.

disburse (verb)
pay out, pony up.
divulge (verb)
admit.
pay (verb)
grant, disburse, put up.
possession (verb)
pony up, spit up.
puke (verb)
spit up.
recompense (verb)
pay.

Other synonyms:

puke
spit up.
Other relevant words:
allow, concede, pay out, pay, admit, own, confess, disburse, acknowledge, spend, grant.