Coffee that has milk or cream in the coffee could spoil overnight due to the milk or coffee creamer turning sour.
However if the coffee is just plain old black coffee without any creamer or milk in it then the coffee should be perfectly fine out at room temperature overnight without spoiling.
I sometimes make a full pot of coffee during the day and sometimes have the coffee leftover for a few days before finishing it up.
I just reheat the coffee in the microwave after adding some water to dilute it and then put the coffee creamer in the coffee to make it taste better.
Coffee as long as it has no milk or creamer in the coffee should not spoil if left out overnight as it usually takes 3 or 4 days before coffee without milk or creamer begins to spoil and grow mold.
I did an experiment before with a foam cup and coffee and left it out on the counter at room temperature on purpose to see how long the coffee would take to go bad and grow mold.
The coffee started growing some mold within 4 days and then a week later it was nearly full of mold and by the second week it really grew a lot of mold and had really went bad.