Just an educated guess, but it appears to be an older loanword from Spanish quince, and considering the word for money is also Spanish in origin (béeso from peso), the use of Spanish to do trade must have resulted in those Spanish words becoming associated specifically with counting amounts of money
This is correct. Diné Bizaad has a few borrowed nouns from the Spanish language. Quince is just one of many. The reason we call a penny "Sindáo" is because it originates from the word "centavos". A nickel is called "łitso" (yellow) because it is said that back in the day the money bill for five cents was yellow. When it comes to talking about money in Diné, there is a lot of history incorporated with their respective meanings.