Real-time merge of two databases on different servers
This sounds like your customer does not entirely understand what is possible with SQL Server. It is also possible that he is confusing SQL Server with Oracle. With Oracle, you can spin up one database and have two database instances running independantly and operating of the same data set. 

With SQL Server, the best you are going to probably do is some sort of Merge replication with two application servers and a distribution database. I would re-visit the customer requirements, determine exactly what he wants, not what he thinks he wants, and not how he wants to do it, and then come up with a solution to provide to the customer. 

Unless you or your customer are willing to buy a third party product, some form of SQL Server replication is going to have to be used. Here are some links (2008 R2):

Merge replication

Replication overview