Is there any difference between the following sentences?
I have coffee on the outside. It is referring to some coffee shop.
I have coffee outside.
Can anyone explain to me which of these constructs is correct?
I have coffee on the outside
This means that you have coffee on the outside of something. This does not mean you will drink coffee outside. For example you might be talking about the colour of paint:
It's painted red on the inside, but I have coffee on the outside.
"It has X on the outside" means that X is on the external surface of something.
If you want to say that you normally drink coffee outside then your second sentence is correct.
If you want to say that this time you will be outside, or that you'd like to be served your coffee outside then say:
I will have my coffee outside.