I am attempting to learn of my family history in Lapland. Eastern Lapland the surname was Karjkold. Western Lapland surname was Koen. When the two families married the surname was changed to Koenkarjkold. I do not know the reason why, but this is what I was told by my grandfather before he passed away. The eastern family was from the Kola Peninsula area and the western family was from southwest of Tromso.
I don't know if this helps any.
It truly seems like trying to find information about those names is like finding a needle in a haystack..
Lapland is a vast area stretching from Norway to Russia and seems that both names has not at any point been registered in Finland as such, "Karjkold" or "Koen", because the Population register center didn't give me any hits. Their database stretches back to the 1800 century.
Now I recommend you to approach the following authorities/ municipalities which I would think could help you on your way. Every town/municipality has it's own parish and the parishes possesses old churchbooks from the time when the population registry was taken care of by the church. I think that by approaching below sources, at least one of them should be able to point you further =)
In your mails you can ask to be fowarded to the correct persons or departments. For example the congregations of the cities should be able to help because the old church books contain a lot of useful info about names, relatives, birthplaces + dates.
Did you also ask this same question from the Russian and Norwegian Expert here on allexperts.com?
City of Tromso - firstname.lastname@example.org
Murmansk city / Kola county - http://www.gov-kola.ru/
Murmansk Christian Church - http://www.murmanskchristianchurch.org/index.php?p=1_19
the Genealogical society of Finland - http://www.genealogia.fi/indexgb.html
Truly hope this helps you on your way and don't hesitate to contact me again if none of the above
gives you any result. Then my Russian work colleague can write you the e-mail in Russian for better understanding =)