Alright. I did something like this in physics class once. A standard penny is .36 cm^3. The diameter of a penny is 1.9 cm and the glass looks to be about four pennies wide and about 5 or 6 pennies tall. I'll go with 5.5. The diameter of the glass is probably 7.6 cm. The height of the glass about 10.45 cm or just 10.5 cm. Volume of a cylinder is V=(pi)(r^2)h. With that being about 476 cm^3, it being tapered down at the bottom + not being filled completely to the top, it could be between 700 to 1000 pennies.
I'll give it wild guess and say 738