Rav Haim Palachi (Izmir, Turkey, 1788-1869), in his work Mo’ed Le’chol Hai (8:6; listen to audio recording for precise citation), mentions a custom to set aside money for needy and humble Torah scholars on Ereb Shabuot. Specifically, one sets aside 91 coins, and then adds an additional thirteen coins, one at a time, for a total of 104 coins, which is twice the numerical value of "Ben" (son). The money, as mentioned, should be given to humble and needy Torah scholars. Rav Haim Palachi writes that this custom serves as a Tikkun (rectification) for the sin of Adam Harishon, the sin of the golden calf, and the desecration of the Berit. Additionally, following this practice is a Segula ("charm") for childless couples to have children.
Our custom is to use US dollar coins for this purpose, and on Ereb Shabuot we designate these coins and the Rabbi then distributes them to needy Torah scholars on behalf of those who made the donation.
When Shabuot falls on Mosae Shabbat, this custom is observed on Friday, the day before Ereb Shabuot.