This bit of US slang for one dollar or money in general now sounds very dated, though it still turns up from time to time, especially in humorous journalistic writing. An example appeared in Fortune in 2003: “Today I make a respectable mound of simoleons at my business job, but they pale, evaporate, and dribble down the side of the countertop when compared with the simoleons Mr. Grasso has accrued in his years of faithful service.” The word was given a boost when it was chosen as the name for the currency in the simulation computer games featuring the Sims.
But it goes back a long way. What follows is a bit speculative, but fits what evidence we have. In early eighteenth-century Britain, the small silver coin whose proper name was sixpence was often slangily called a simon. We’re not sure why, but a plausible origin lies in the name of Thomas Simon, a famous seventeenth-century engraver at the London Mint who designed some new coins after the Restoration in 1660, including the sixpence. (A New Testament reference, to St Peter “lodging with one Simon a tanner”, led to the coin later being called a tanner instead.) Simon seems to have been taken to the USA and transferred to the dollar coin (the name is said to have been recorded in the 1850s). Having in mind the much more valuable French gold coins called Napoleons, some wit bundled simon and Napoleon together and made from it simoleon.
The first example I know of is from the Davenport Daily Gazette of Iowa in 1883, in a piece of mock-Biblical whimsy about the local journalists losing their press club to an upstart incoming dentist who offered their landlord more money: “The doctor spoke unto Mr. Thede, and did offer to him many fat simoleons and talents of gold and shekels of goodly silver, and Mr. Thede hearkened unto his voice, and the tones thereof were too canny for him.”