Eggs are great for breakfast! Bacon is also a good choice if you're avoiding carbs.
If you like fruit, raspberries, strawberries, and cranberries seem to be the best options. They have carbs but they're among the lowest amounts for fruit.
And heck, for breakfast, I don't go by the norms. Lately I've been having cauliflower and cucumbers with this fiesta ranch. The ranch has carbs but it's a very small amount because it's a mix and I add it to sour cream.
I also sometimes will eat string cheese.
I don't drink coffee, so I don't have much advice about what to put in your coffee. My dad, who used to be diabetic, uses "sweet n' low" in his coffee, which is saccharine, an artificial sweetener. One packet has 1 carb and apparently the liquid version has none.