aviary; birdhouse
A structure for keeping birds, often larger or more varied than a simple chicken coop.
There are many rare birds in the zoo's aviary.
henhouse; chicken coop
Specifically a small house for chickens or poultry; often used in farming contexts.
In the morning, I collect eggs from the henhouse.
巣箱 is a nest box or birdhouse, often smaller and for wild birds, whereas 鳥小屋 is a larger enclosure.
Compound of 鳥 (tori, 'bird') and 小屋 (koya, 'hut' or 'small house'). The reading とりごや follows rendaku voicing of こや to ごや.