In this case, I probably would have had a difficult time finding them if you hadn't had that Fred's father was from Apenrade. From there I found the passenger list and them it was simply a matter of looking in the parish records. The Danish parish records (including the areas of Schlesvig that ended up as part of Denmark) are available (free) online at http://www.arkivalieronline.dk/default.aspx
You have to browse and some images are much clearer than others and of course it's handwritten in Danish, but they have, for instance, the parish records for Rise parish back to 1748. (some parishes back to the 1600s)
I've attached the birth/baptism record for Fred/Fritz and Karen Marie Claudiana/Mary Claudina Nielsen so that you can see what they look like. (Mary's is especially faded and difficult to decipher - most are not that bad) Mary's parents marriage record too. (Fritz is #32, Karen Marie/Mary is #27 and Jens Nielsen and Ane Margrethe Pedersen are #3 on the respective images.) Note that on the marriage record it gives both of their birth places/dates. Jens was born in Vennerslund -which is a sted in Stadager parish- on Jan 22 1847 and Ane Margrethe in Øster Kippinge on Mar 28 1846.
...and I'll leave it at that assuming that you'd prefer to do your own searching. Just one more site that you might find useful http://www3.sympatico.ca/colin.swift/danish.htm
This takes you to Norman Madsen's mini Danish/English dictionary - but do take a look at the other info and links there. It's a wonderful site with lots of good info and links.
Best of luck,