Family planning information cards are only for women of childbearing age, just like men, and generally only require relevant marriage and childbirth certificates. Therefore, you can do this.
You can go to the original unit to write a certificate that you are unmarried and childless from XX to XX. Then, you can take this certificate, marriage certificate, ID card and household registration book to the township or county-level family planning department where you are handling the one-child birth service certificate. If they don't agree, then you can only do so.
Go to the civil affairs department where your registered permanent residence is located in Shanxi, and issue the unmarried certificate of XX to XX, and issue the childless certificate to the family planning department where your registered permanent residence is located. With this certificate at or above the county level, marriage certificate, household registration ID card and other related certificates, you can apply for the one-child birth service certificate.