Answer
$1.77\times 10^{-8}\;\rm C/m^2 $
Work Step by Step
We know that the electric field of an infinite plane of charge is given by
$$E=\dfrac{\eta}{\epsilon_0}$$
Let's assume that the radius of the penny is much greater than the distance between the penny's surface and the point at which we measured the electric field. And let's assume that the surface of the penny is perfectly flat which means that its surface charge density is uniform.
Now we can consider the penny as an infinite plane of charge.
Hence, its surface charge density is given by
$$\eta=\epsilon_0 E$$
Plugging the known;
$$\eta=(8.85\times 10^{-12})(2000)$$
$$\eta=\color{red}{\bf 1.77\times 10^{-8}}\;\rm C/m^2 $$
