TIme needed: 198 years.
All you really need to know in order to be able to solve this problem is what exactly is a Coulomb.
A Coulomb is a unit of electric charge equivalent to the charge contained by
So, to get a total charge of 1 C, you need the body to give out a total of
You know that the body gives out
To get a better understand of exactly how much time is needed, use a series of conversion factors to go from seconds to years
This is equivalent to
SIDE NOTE I'll leave the answer rounded to three sig figs, just for good measure.