An alternative solution that did work.
1, Create a .pem file from the original .p12 (enter password when prompted)
openssl pkcs12 -in my.p12 -nocerts -out my.pem -nodes
2, Create the request from the .pem:
openssl req -new -key my.pem -out my.csr
You will be prompted to enter country, state, locality, organisation, unit and common names and your e-mail address, and extra attributes (challenge password and optional company name).
Done.
EDIT: also on CERN Certificate Authority's Prepare renewal certificate signing request(CSR) with OpenSSL.