Instead of AMO, you can also directly issue XMLA ALTER statements. Actually, AMO converts everything to low level XMLA as well, which are then sent to the Analysis Services server. However, the official documentation of the XMLA ALTER statement at http://msdn.microsoft.com/en-us/library/ms186630.aspx is difficult to read. It would be easier to capture the XMLA statements resulting from the AMO issued by BIDS when you click deploy. You can do this via SQL Server Profiler as documented here: http://technet.microsoft.com/en-us/library/ms174946.aspx.
And, as soon as you have more than a few trivial changes, it may be much easier to re-deploy the complete Analysis Services database instead of capturing just the changes and trying to create ALTER statements.