Is it permissible to give a divorced sister who has no job or child a sum of money that was vowed to Allah Almighty for the purpose of having a child?

If you made a vow to donate a specific amount of money as charity upon Allah granting you a child, then fulfilling this vow is obligatory. This is based on the Prophet's (peace be upon him) saying: "Whoever vows to obey Allah, let him obey Him; and whoever vows to disobey Allah, let him not disobey Him." It is preferable to give the amount to your sister if she is poor, as it combines charity with maintaining kinship ties.