The openssl req command proposed by @Tom H is correct to create a self-signed certificate incl. password-less private key:
openssl req -nodes -new -x509 -keyout server.key -out server.cert But: the trick to create a private key without passphrase is -nodes in the command ("No DES encryption please!"). Omitting -des3 as proposed by @MadHatter is not enough!
(Details: Omitting -des3 is enough for the openssl genrsa ("create a private key") and openssl rsa ("convert a private key") commands. Just not for for openssl req.)