How do I share CookieContainer between two Web Service clients?

Question

I have two WCF Web Service clients, which are generated by the "Add Service Reference" wizard:

    public partial class DataSourceServiceClient : System.ServiceModel.ClientBase<DataSourceService>, DataSourceService {
...

I would like to share the same instance of CookieContainer between them, to reuse the same HTTP session.

How do I do this?

I could not find any CookieContainer property in the client or ChannelFactory.