Yes, anyone can contribute to a Coverdell Education Savings Account on behalf of the designated beneficiary.  You do not have to be related.  

You can make a contribution to a Coverdell Education Savings Account as long as your income does not exceed these MAGI limits: 

There can be multiple savings accounts established for the same child as long as the $2,000 annual limit is maintained.  This is the total of all accounts directed to one child in a calendar year.