I don't know who the genius is that brought coffee and smoothies together, but I would thank them personally if I could. Unfortunately, in the same way coffee wakes you up in the morning, it also wakes up your digestive system.
Everybody's tolerance to caffeine is different, but most people are safe with one or two cups per day. As long as you keep it in check, a little coffee in your smoothie shouldn't be an issue. If you do notice that you need to go righthisminute, try a coffee-free smoothie like this one.