In Japanese, you can often use possessors (well, genitive descriptors) where in English we might expect a prepositional phrase with a little bit more semantic content. This happens really quite a lot - take a look at these:
前の人 'the guy from before'
奥の部屋 'the room in/at the back'
Your specific example follows the same kind of pattern - the 台所 has something to do with the morning; exactly what is left up to context. The translation you're given isn't necessarily the best reflection of the structure; it might be better as 'the kitchen in the morning smells like coffee', with 'in the morning' directly modifying 'kitchen'.
A somewhat analogous construction in English might be 'the morning coffee' or 'the evening news' - it's not that the coffee belongs to the morning, it's just coffee that you drink in the morning. An even more direct translation of that sentence, then, might be 'the morning kitchen smells like coffee', though that's certainly odder in English.