Can we drink coconut water multiple times a day?

Yes, you can drink coconut water 2-3 times a day, unless you are diabetic.

Keep in mind the following few things -

• Coconut water should be fresh, not packaged
• In case you are diabetic, please do not consume coconut water (as it is sweet and may increase blood sugar levels). Focus on non-sweet juices such as green juice, ash gourd juice, cucumber juice, etc. 
• Don't drink even coconut water if there is no physical need for it. Remember, you are on a fast. You should consume juices/coconut water only when you feel thirsty/hungry.