Here are few other paper money issues made in the 18th Century.
Isle of France and Bourbon - The governing body of the Isle of Bourbon issued paper money notes in 1766 for the Isle of France and Bourbon, denomination was 40 sous tournois.
Russian Empire - The State Assignats introduced paper currency into the Empire in 1769, denomination included 25, 50, 75 and 100 rubles and in 1787 the 5 and 10 rubles were added. The value of these notes were never stable it was later on in the 19th century that this was taken care of by fixing the values.
The German State of Saxony - In 1772 the Royal Electoral Saxon Treasury issued paper money notes, denominations were for 1,2, 5, 10, 50, 100 reichsthaler.
Iceland - The Courant Bank issued 1 and 5 rigsdaler notes in 1778: Iceland was a very oppressed state during the 18th Century, what with the Danish strict trade restrictions and the English and Spanish pirates who raided their coast continuously.
Netherlands East Indies - In 1784, the United East India Company issued paper money notes in denominations of 25, 50, 100, 200, 300, 400, 500, 1000 rijksdaalders. Netherlands is known to be the first truely capitalist state in Western civilization, they introduced insurance, went through the first national boom and burst, ran a stock market and issued stocks.
By the time the rijksdaalder notes were issued the company was already in decline, the United provinces in the Indies and Great Britain were already at war. The company was actually in financial difficulties, the paper money notes were probably issued to combat this but the company never recovered from this.