The following datas I have got from
http://ddss.nu/ and they have an English version. The database has many parishes in the provinces of Halland, Skåne and Blekinge but not all. The parish of Jämshög is situated on the northwestern corner of Blekinge, close to Skåne and the province of Småland (you can maybe find a place Olofström there which today is the main place in the area).
Sven Håkansson, born Feb 20, 1858 at Rösjö, parish of Jämshög. Parents: Håkan Andreasson and Bengta Larsdotter.
Hanna Nilsdotter, born Mar 19, 1853 at Brännarebygd, parish of Jämshög. Parents: Nils Ingwarsson (also Ingvardsson) and Bengta Persdotter (29 years old), married Dec 28, 1849.
Håkan Andersson, born July 19, 1831 at Jämshög No 7, parish of Jämshög. Parents: Anders Jonasson and Maria Henricsdotter (34 years old).
Bengta Larsdotter, born Febr 21, 1831 at Snöfleboda, parish of Jämshög. Parents: Lars Jönsson and Elna Månsdotter (21 years old).
As you can see quite often they stated the mothers age which can be some help. One Elna Månsdotter, born Mar 18, 1810 at Öfra Glumslöf in the parish of Glumslöv in Skåne, not so far from Jämshög, parents Måns Åkkerman and Ingebor Månsdotter. But to be sure of that this is correct you have to check the original books or microfiche. It can be hard from Minnesota (they have them in Rock Island, Illinois, but that is not so close).
In any way, good luck for you hunting