In SQL Server 7.0 and 2000 database diagrams information has been stored in table dbo.dtproperties, you can use DTS to transfer diagrams.
Since SQL Server 2005, the system table dbo.sysdiagrams holds the information of database diagrams created for a database.
When transfer database diagrams between SQL Server 2008, the tables in the database referred in the diagrams should have the same structures in both SQL Servers or databases.
By using SQL server Import and Export data tool to copy data in dbo.sysdiagrams table, once done refresh Database Diagrams you will see the diagrams.