Did you drink coffee while pregnant? An article I read on Kellymom awhile ago said data showed that if you drank coffee while pregnant, than your baby was less likely to react to it postpartum.
Are you especially sensitive to caffeine (drink it at 2pm and have trouble falling asleep)? I am. It's called "slow-metabolizer", and I wonder if I am whether my kids might be too.
In any case, I drank a small amount (half a cup to a cup) while pregnant and continued that amount while breastfeeding and didn't find it interfered with sleeping (though nursing before a nap sometimes did seem to perk my baby up - couldn't be sure if was the caffeine or the calories).
The amount a baby cries increases from day 1 to about week 7 or 8, as they sleep less and try to adjust to life outside the womb.
So, unhelpfully, I'd suggest the caffeine could be the culprit, or it could be something else or everything else (as in "just a phase").
You could try weaning yourself from the caffeine in the coffee (I switched to half-caf), or going without for just one day, to see if it makes a difference.
If you enjoy / would like to continue breastfeeding, I would try solving the crying & sleeping problem first (trying to put baby to sleep at first yawn, for example, in case he/she's getting overtired and then crying/fussing at naptime) and not jump to abandoning nursing as the only course of action.
Good luck!