I have that coffee problem as well. I think its really a caffeine problem though.
I did some searching when i first noticed the same thing as you, it struck me as i drink black coffee and found my sugars would rise, stay up, and then as the caffeine wore off some hours later my sugars would drop drastically quick with that event.
If you search the net you will find that some websites/research claim caffeine interrupts the bodies ability to absorb insulin (for some people), and because of this it causes your sugars to go up if you have coffee within a couple hours of food because your body can't absorb the insulin your injecting to counter the food you just, or about to eat.
I used to have my black coffee every morning about 30-40 minutes after eating, and found that my sugars would go up as they normally did after my meal, but instead of coming back down they would go up another 1-2mmol/L and then stay there.. So i would go from 5 to 7 post meal, then up to 8.5 and they would sit at 8.5 for another hour or 2 and then sharply drop back to 5 about 2-3 hours post coffee..
My solution to this is to inject, wait my 20 minutes, eat breakfast, and then 1.5-2 hours later once the insulin has started going full speed ahead THEN drink my coffee. I have found that this doesn't affect me nearly as much.. Its almost as if coffee freezes my sugars in place for 2-3 hours lol
Try experimenting with your timing, and see what you can do to make it all work.