The idiom dates again to the 16th century and is claimed to be a corruption of “legem pone”, the primary two phrases of Psalm 119 that used to be sung on English quarter day, when money owed had been settled and bills had been made.
The time period become related to bills and therefore used to be used as an expression for “money down”.
Its meaning used to be first recorded via Thomas Tusser in Hundreth Excellent Pointes Husbandry in 1570: “Use Legem pone to pay at thy day”.
The time period “pony up” itself used to be first utilized in print in a Connecticut newsletter The Rural Mag in 1819.
Curiously, regardless of its English starting place, it’s recognized to be an American word.