Upto 300 mg caffeine per day doesn't cause any problems for the baby. One cup of 8oz has about 100 mg caffeine. So 2 to 3 cups a day are perfectly ok
Next Steps
Caffeine is also contained in tea, all sodas, chocolate
Health Tips
Better to have the caffeinated drink after a feed. That gives an interval of about 3 hours before the next feed, minimising content in miilk