Seeking happy immigration songs: I will mostly write below about the Irish tradition as it is the one I know best, but the invite is for songs from any background.
The Irish have hundreds of sad songs about emigration. Many are about love and longing for the homeland. Some complain about conditions in the new land - prejudice, being pressed into armies, hunger and hardship. I also know some similar Scottish songs, including a few in Gaelic.

It has always seemed a bit curious to me how popular these songs are in Ireland, among not only people who have returned home but among those who never emigrated. It is almost as if, in a small country with a high level of emigration, we console or re-assure ourselves that we have made the right choice staying at home.

Literature and drama, on the other hand, tells a more complex tale where the emigrants are ambivalent about their homeland and glad to escape poverty, oppression or just to have more freedom of self-expression in a more open society. So why isn't this expressed in song, - or is it?

Off hand I can think of a couple of songs of happy immigrants - the fanciful "Oleanna" and that one that goes "When I first came to this land, I was not a wealthy man, But the land was sweet and good and I did what I could". I think both are songs from Scandinavian immigrants to America (?). A couple of more recently composed songs also spring to mind. "Indiana" tells of someone returning to Scotland although he's made a good life there and friends tell him he's crazy 'going back to such poverty' and there is a line in "My Father's Immigrant Eyes" saying that the father has 'given [the singer] this country'.