Collocations for cottage - noun

humble, little, simple, small, tiny
charming, cosy/cozy (esp. AmE), picturesque, quaint
country, rural (esp. BrE)
derelict (BrE)
half-timbered (esp. BrE), stone, thatched, wooden
rented
farm (esp. BrE), tied (BrE) (= owned by a farmer and rented to a farm worker)
They lived in a tied cottage on the estate.

holiday (BrE), summer, weekend (esp. BrE)
guest
They put us up in a guest cottage next to their house.

have, own
It was her dream to have a little cottage in the country

live in, stay in
We stayed in a cottage on a farm.

rent, take (BrE)
We rented a cottage for a week.

build
They built a small guest cottage on their land.

let (BrE)
buy
sell

home
garden
industry

in a/the cottage