Anders Andersson

The birth record of Carl Emil points the confessed father out as ranger (banvakt/are/) Anders Andersson from Köpung, who can be found on picture 205/page 201 in Frykerud AI:25.

He became a widower on Jan 16, 1874, and was married 2ndly Dec 26, 1875, with Kristina Andersdotter, 1845-1908.

Carl Emil was born in October, so Anders had his meeting with Anna Svensdotter fairly short after his wife's death.

No father is implied in the birth records for Anna's two sons named Gustaf, and Anders is in hos second marriage by then, so it's unlikely that he was their father as well.