First a short aside on terminology; "Finnmark" is a region of Norway and in Norwegian "Finn" has been used as a term for Sámi/Lapps. For the general area inhabited by Sámi the term Sápmi or Lapland is used. Use of the term Finnmark for Sámi areas outside Norway is a bad idea since the term Finnmark is also used in Swedish for areas settled by the Forest-Finns. (who were Finns and not Sámi)

Päiviö (or Peder Päjviä by Tornaeus) and other variants, was a 17th century Sámi shaman/magician (by Tornaeus dead c.1670) and semi-legendary figure about whom there are a number of Sámi folk tales. (particularly Inari-Sami) He was also supposedly the founder of the clan of all the people with the last name Päiviö. One is about his duel with the magician of Inari where he won and became the most powerful magician. There are other stories about him having heard that Christianity would destroy magic and baptism make magicians ineffectual, whereupon he traveled to Stockholm to ask the king to help convert Inari so he would become the most powerful magician. He's not portrayed as an enemy of the Sámi.

Anyway the oldest documented story (by Tornaeus) is the one where Päiviö is having great troubles with a plague that is killing his reindeer, and so he makes increasingly large sacrifices to his village idol, dragging heaps of food and lumber and reindeer heads and horns, and after a day of prayer having received no sign from the gods he gets so angry he burns the whole lot up. When the other villagers got angry about it he supposedly said "let the idols avenge themselves on me" (in a parallel to the Bible; Judges 6:31). He converted to Christianity and sent his son Vuolab or Vuolapi (Vuollaba in Tornaeus' spelling) to Inari to do the same to their sieidis. Which he did, and then fled to Norway.

As said though there are other stories and other versions of the conversion story. As they're written post-conversion they all reflect a positive view of Christianity though.

The most detailed work seems to be (I'm afraid I don't have access to it) the Finnish folklorist/historian Toivo Itkonen's paper Päiviö Ja Vuolab (Lapin Sivistysseuran julkaisuja. no. 25) from 1963, also published in Kalevala-seuran vuosikirja 43

Johannes Tornaeus, Beskrifning, öfwer Tornå och Kemi lappmarker, p28-29, 1672 (digitized)

Hugo Samzelius, Sagor och sägner, skrock och öfvertro från finnbygder och lappmarker, 1902