I had a customer exploring this, and ultimately we came up with the following. The cert and key are pushed in two separate calls:
SSL Cert Push
curl -vvv -k -H "Authorization: A10 `./APIauthv3.sh 10.22.10.54`" -F "json=@filessl.json;type=application/json" -F "file=@local_cert.pem;type=application/octet-stream" https://10.22.10.54/axapi/v3/file/ssl-cert
SSL Key Push
curl -vvv -k -H "Authorization: A10 `./APIauthv3.sh 10.22.10.54`" -F "json=@filessl_key.json;type=application/json" -F "file=@local_key.pem;type=application/octet-stream" https://10.22.10.54/axapi/v3/file/ssl-key
Attached is the Auth script as well as the filessl and filessl_key json files. The expected response is a HTTP/204.
axapi-files.zip (676 Bytes)