I have searched for Any Ursilla/Ursulla, Urs*, born plus/minus 5 years in every census 1870 to 1910. I searched for all of the children, using Ing*, Ann*, Agn* and Gus*, with born plus/minus 5 years born in Sweden. I searched for any Olav/Olaff/Ole/Ola, last name beginning with Guf*, Gus*
I did have ONE very remote possibility.
The 1870 Census for Barre, LaCrosse County, Wisconsin
Ole Gufusen, age 33, born in Sweden
Usuol, age 34, born in Sweden
Idabel, age 11
Anka, age 9
Anna, age 7
Gustaff, age 3/12. born March 1870.
--I have seen many Swedish immigrants having language misinterpreted by the census enumerator. My own "Bystrom", was in the census as Beesthraumn. In this case, the ages are correct for Olof and Ursilla. Ingeborg as Idabel, Anka is Agnes but the age is not correct. Anna would be Annika at about the right age. The Gustaf born March 1870, would be a typical re-use of a name for a child that had died.
--This of course is my speculation and there is no proof, at this point. But, I have seen this spelling/Swedish accent problem before.
Now then, I thought I had answered this yesterday with additional suggestions, but they do not seem to be present.
What additional information do you have that might help in the search? Any family lore about where they went? What names they may have used? You have identified their departure as being 9 April 1869. Is this from a parish record for leaving the parish, or a ship manifest? Olof left two years earlier as it appears, again from where is this record?
Have you contacted local Swedish sources for information as to their destination? Here are some websites that might hold some records for you in Sweden.
Good place to start: http://genealogy.about.com/library/authors/ucolsson1g.htm
12 pages of info.
National Archives of Sweden: http://www.ra.se/indexengelska.html