"Pennies are money too; they spend just as easy as the rest of them." I told her "Well, someone needs to tell that guy across the street that, because he wouldn't take my pennies." Eventually, I fed my cats their penny bought food and made it to work with a couple of minutes to spare. I couldn't stop thinking about that situation all day. So much so, I began to research whether or not that guy had the right to refuse penny payments. It turns out, he did.
Title 31 (Money and Finance), Subtitle IV (Money), Chapter 51 (Coins and Currency), Subchapter I (Monetary System), Section 5103 (Legal Tender) of the United States Code states:
United States coins and currency (including Federal Reserve notes and circulating notes of Federal Reserve banks and national banks) are legal tender for all debts, public charges, taxes, and dues. Foreign gold or silver coins are not legal tender for debts.
In the words of the United States Treasury, what this statute means is that "all United States money is a valid and legal offer of payment for debts when tendered to a creditor. There is, however, no Federal law mandating that a person or organization must accept currency or coins as for payment for goods and/or services."
So basically, if the cashier at that convenience store doesn't want to take pennies at all, or they want to be paid in nothing but quarters or nickels, they are entitled to do so, but they should specify what their payment policies are before entering into transactions with their customers. For example a sign that states: We do not accept payments made exclusively in pennies. It would conveniently fit right next to the sign that states: We do not accept bills larger than $20.