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The exact number would depend on the shape of the container and how the pennies packed in, but assuming that you are referring to US Coins and US gallons (as versus Imperial Gallons), I'd estimate the answer to be that about 20,000 pennies can fit in a 3 gallon container.
Calculation is as follows:
1 US gallon = 0.133680556 cubic feet
1 US penny has a diameter of 0.75 inches and a thickness of 0.061 inches
The most efficient pack would be if the pennies were stacked in columns and if those columns were pressed so that each column touched six others. But lets assume that the coins were just poured in, and so packed more like columns on a grid (i.e., each column touches four others). This means that each penny takes up 0.75*0.75*0.061=0.0343125 cubic inches of space (including its actual volume and its estimated share of the dead space in the container. This equates to 0.0000198568 cubic feet, meaning that 0.133680556/0.0000198568 = 6732.24 can fit in a gallon. 6732.24 times 3 is 20,196.72; thus my estimate of about 20,000.
Note that if you were prepared to melt the pennies so as to fit more into the container (i.e., no dead space), the volume that you would use for each penny is ((0.75/2)^2)*PI*0.061, allowing you to fit 8571.754788 melted pennies into each gallon, or 25715.26436 in a three gallon container. This would, however, make it very difficult to cash the pennies in at the bank later!
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