private readonly ReportingService2010 _rs = new ReportingService2010();
The type or namespace name 'ReportingService2010' could not be found (are you missing a using directive or an assembly reference?)
Either create a proxy class and include it in your application or add a web reference to ReportingService. The tutorial is available there:
Note that if you are going for proxy class and you are using more than one endpoint (ReportExecution, ReportingService) you should generate proxy classes on different namespaces, otherwise you will get clashes.
Did you do it by web reference? If so, try using WSDL at the command line. Command line syntax:
wsdl /language:CS /n:"Microsoft.SqlServer.ReportingServices2010" http://serverName/reportserver/ReportService2010.asmx?wsdl