Replication of several databases to several databases on one server

Question

I am at a loss of what to do.  Here is what I am working with and what I want to accomplish:

We have one godaddy server.  We have several servers on local machines, running mysql. We want to set it up so that each local machine replicates a certain database to a database on the godaddy server. 

I can not figure out how to do this, nor can I find any helpful documentation.
I'm happy to provide more information if it is needed.