sick with the money, I can cough a stack, I can sneeze some Gs

He is bragging that he is "sick" with the money, meaning that he has a remarkable ability to earn it. Since he is "sick with the money," he then makes a pun about it (the "cough" and "sneeze" lines; people cough and sneeze when they are sick, of course).
eastcoastchris87
It's a play on words. Sick means crazy cool or insane meaning he has a lot of money. Sick also means like you're sick, you got a cold so he's got such a bad cold that he coughs up a whole stack of money and sneezes gs (grands... $1000) so lots of money.
love__jones
He has so much money that it has infiltrated his body like an infection. When he coughs, a stack of dollar bills comes out of his mouth, and when he sneezes, thousands of dollars are expelled from his nose/ mouth.
frankricard
He's saying that he has so much money that he can cough out a stack of bills or sneeze out thousands of dollars (a G is $1000)
Tenshi
comparing having money to sickness so as he gets progressively sicker his wealth increases as well
snick3rz
he's bragging about his money making abilities. when he coughs he can make a stack, a pile of money, he can sneeze some thousands dollar bills(Gs=a grand.
decyphring fo f...