Found another one:
"admin_signup_mode_invite": "Nur auf Einladung",
"admin_signup_mode_approval": "Durch Bewerbung (mit manueller Freigabe durch einen Administrator)",
for approval there is an equivalent for the first and it would be
“Nur auf Anfrage (mit manueller Freigabe durch einen Administrator)”
Your sentence can be used but it depends: “Bewerbung” is like a job application where you battle with others and have to “Advertise yourself”, I guess that matches in the sense of writing what you will post but the general words are
“Einladung” and
“Anfrage”
[like invitation/request]
@sl007 just to be clear, my level of German is "I know the pronunciation rules and about 30 words" :D
This translation is by @lioh