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 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...
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