Does the wife's statement, "If I sell my gold, I will donate its price as an ongoing charity (sadaqah jariyah)," constitute a vow, and is it permissible for her to purchase shares in cooperative societies and later donate their profits, equivalent to the value of the sold gold?

The wife's statement promising to donate the value of the gold is not considered a vow (nadhr). If she does not fulfill it, there is no sin upon her, but it is better for her to fulfill it. It is permissible to buy shares in a cooperative society and donate its profits if its activities are lawful and do not involve usury. Expediting the charitable giving she intended is better, as it is a hastening towards good.