According to Bulbapedia the size of a Pokeball switches between that of a baseball or a ping pong ball by pressing a button. My calculations will be under the assumption that the pokeballs are full sized.
Diameter of Pokeball = 75mm (From Wikipedia)
Volume of Pokeball = 2.21 * 10-4 m3 (vol. of sphere)
Height of Coit Tower = 64m (From skyscrapercenter.com)
Diameter of Tower ~= 11m (measured from Google Maps)
Volume of Tower = 6082.12 m3 (vol. of cylinder)
The Pokeballs are packed in a HCP lattice to produce highest average density of 74% of total volume (From Wikipedia)
74% of Volume of Tower = 0.74 * 6082.12 = 4500.77 m3
Amount of Pokeballs = Total volume occupied by balls / Volume per ball
= 4500.77 / 2.21 * 10^-4 m3
= 20,365,475 Pokeballs