I typically bring about US$500 cash for emergency and secure it in a hotel safe. I rely of ATM to get all cash I need in Jamaican currency - I recommend ATM to get best possible exchange rate. I never had any problems getting cash out of ATM last month, except I had to go to Scotia bank at downtown circle a couple time when Time Square ATM was out of cash. My wife carries another debit card for me as a spare, but never had that problem in our 25years of travel to Ja.
Advise letting all your credit card and debit card providers know you will be in Jamaica, and be aware of your maximum daily ATM withdrawal limit (typically can be anywhere from US$300-500 per calendar day).