Can a husband offer money or property to his first wife so that she agrees to polygyny?

Giving a gift as a sign of love is not wrong, but making it the price of consent can taint the honesty of the process and your wife's heart. A wife who agrees because of money may regret it later, and the husband may think his obligations have been paid off. Maintenance (nafkah), housing and the rota (turn of nights) remain obligatory after marrying again; they are not something that can be traded for a lump-sum gift. If you want to protect your wife, discuss real protections, for example transferring the house into her name or setting aside savings for the children, and do it for the sake of justice, not to buy an answer. The court will still hear your wife's own view. See protecting property rights.