I don't see him in 1880. I also tried in 1900. Is there a reason why you think he immigrated between 1879 and 1881? I can try a search for him in 1880, with no surname, but with such a common first name, it will be difficult.
The more information we have, would make the search easier. Some of the search options for 1880 include: first name, birthplace, estimated birth year, mother's and father's birthplace, occupation, residence (including state, county and township).
There are very limited 1890 US census returns, due to a fire.
If he arrived c1880 he may not have gone directly to Montana. If he arrived in America prior to the 1880 census, he could be residing in any state.
I don't see "Caroline" or "Carrie", living in Butte in 1900.