I would like to do the following all in memory without writing to disk on the client's machine.

Zip an in-memory DataTable in .NET 2.0 (C#) to memory (not disk).  Then I'll send it ( string/byte/stream ..  whatever it's called) to our web service.

 I found some code to change the DataTable into a stream, so I think that's the first part. thanks!

 You can use a MemoryStream or a StringWriter with these overloads to keep it all in memory.

string result;
using (StringWriter sw = new StringWriter()) {
   dataTable.WriteXml(sw);
   result = sw.ToString();
}

If you don't actually need a string but read-only, process able XML, it's a better idea to use MemoryStream and XPathDocument:

XPathDocument result;
using (MemoryStream ms = new MemoryStream()) {
   dataTable.WriteXml(ms);
   ms.Position = 0;
   result = new XPathDocument(ms);
}