The first means '[There is no milk in my coffee.] Can you add some [but not much - only a little]?'
The second means '[There is no milk in my coffee.] Can you put some in [using your own judgement to decide on "a normal amount"']
If there's already milk in your coffee, it would be either 'Can you add some more?' or 'Can you add a little more?', with no big difference between the two. I think, if I were saying it, the difference would be this:
Scenario 1: the person pouring has already added what they consider is an unusually large amount: Me: 'Can you add some more?' [meaning 'Go on, I want it really weak.']
Scenario 2: I've been handed coffee with milk in it [that is, the 'pourer' has finished.] It's not quite enough: 'Can you add a little more? [but not too much.]'
But this difference - if I'm not dreaming it - is very slight. Others may disagree, and for many people the two versions may be interchangeable.