Is there an actual age limit on coffee like it is on alcohol ?

No specific law, but watch the amount, because the higher caffeine content on a small body could lead to heart palpitations, sweating, and breathing problems as their adrenaline surges and their blood sugar is spent through. Then any resulting health issues would be potential for reckless endangerment or negligence, just like if you left a child in a hot car only for a few minute, you could still be charged with a crime even if they weren't harmed.

Something diluted like an iced mocha wouldn't be terrible, or only a few sips of coffee, but I wouldn't give anyone under 12 a full cup of coffee.