The Presidential Dollar Coin act had the hopes of saving money by a swtich to coins instead of paper. Minting a Coin is cost offection over printing dollar bills. But "bad money drives out good", and so the dollar coins are little used. so here's the suggestion.
Each of the 12 regional Federal Reserve Banks is permitted to issue up to 300,000,000 one dollar Federal Reserve Notes each calendar year.
Each of the 12 regional Federal Reserve Banks is permitted to issue up to a total of 400,000,000 one dollar and five dollar Federal Reserve Notes each calendar year.
Further, in issuing these Federal Reserve Notes, they shall be delivered to member banks (not to other Federal Reserve Banks).
The last item is in line with the original intent of the Federal Reserve System, and the way the banks seemed to operate for the first 70 or 80 years. Now it’s common to find brand new sequential bills issued from Atlanta in the middle of Ohio or Charles Town, West Virginia.
The 3.6 Billion one dollar bills are more than are currently being issued each year. This does not change anything today, or tomorrow. Sometime in the future it would start to save the government some money in printing cost. Indirectly it will encourage the use of one dollar coins and electronic payments.
To accelerate this, maximum number of bills issued per year could be lowered. Say 250 million ones per FRB, and /or 325 million one and five dollar notes per FRB.