Hi John,
A shortened version of my original reply. I don't know what happened to it.
I rang the Landesarchiv Schleswig Holstein for you and spoke to a woman there. She said that all birth, marriage and death registers are still with the relevant Standesämter. Another possibility of finding out more is to get in touch with the Landeskirchenarchiv.
This is the page of the Standesamt in Kiel:
http://www.standesamt.com/urkunden.php?standesamt_id=4524&q=Standesamt%20KielThe page is in German, but on the righthand side you can see "Kontaktadresse". I would write to them with a copy of the certificate you have and ask them to search for a relevant marriage certificate of the parents. Normally a certificate costs about 10 euros. I don't know whether they charge a search fee. You can write to them in English. Almost everyone in Germany speaks fairly decent English.
The other possibility is to write to the Kirchenarchiv and ask about the parish registers:
Address:
Nordelbisches Kirchenarchiv,
Postfach 3449,
24033 Kiel
Telefon: +49 / (0)4 31 / 64 98 60
Telefax: +49 / (0)4 31 / 68 08 36
E-Mail: archiv.nka - at - nordelbien.de (I've changed the at-sign in case that was the reason my message was not posted).
Again, I don't know whether a fee or a donation is applicable.
I couldn't make out the religion on the birth certificate. it seemed to start with a "d", which is strange. It doesn't seem to be "evangelisch" or "katholisch". I presume the parish registers mentioned above would only apply for German Protestants.
This is the email address of the town archives in Kiel. I don't know whether they have any relevant records:
Stadtarchiv-at - LHStadt.kiel.de
As I said above, for "at" use the usual sign.
There are hardly any parish registers online in Germany. Only Baden-Württemberg has its 19th century parish registers online for free. Mind you, hardly anyone can read them. I've taught myself but it's still very difficult.
I've made a note of the names and will keep my eyes open when I'm on German sites. If I can help you in any other way, let me know.
Best wishes,
LEP 1950