User-defined CLR data types are not supported on Windows Azure Database. Relevant documentation:
Windows Azure SQL Database does not support user-defined common language runtime (CLR) data types.
Source: Data Types (Windows Azure SQL Database).
The following features that were new to SQL Server 2008 are not supported by Windows Azure SQL Database: (...) Extension of spatial types and methods through Common Language Runtime (CLR)
The following features that were new to SQL Server 2005 are not supported by Windows Azure SQL Database: (...) Common Language Runtime (CLR) and CLR User-Defined Types
Source: SQL Server Feature Limitations (Windows Azure SQL Database).
Alternatives:
1) Change the application to use only data types supported by Windows Azure SQL Database. Downside: requires code and database changes. Upside: hosted, highly available service.
2) Use an on-premises or third-party SQL Server. Downside: you have to host SQL Server yourself or pay someone to host it; latency may be an issue; availability and management is your concern. Upside: full SQL Server compatibility.
3) Host SQL Server in Windows Azure Virtual Machines using VM images published by Microsoft. Downside: management is your concern; high availability requires additional configuration. Upside: full SQL Server compatibility; low latency; highly available infrastructure.