What is the ruling on delaying the sale of a piece of gold to donate its price due to inability to sell it or find the poor, and is it permissible to donate its value without selling it, or to fast three days instead?

If you can authorize your husband to sell the piece of jewelry and donate its price, then do so. Do not tell him the reason for the vow. You can avoid his questions by saying: "Not every vow has a reason." A suspended vow is disliked, while a vow of charity is desirable. It is permissible to keep the gold piece and donate its price because the intention is to donate its price.