I have created a SharePoint portal in which I can create  sub sites programmatically up to two level . These sub sites also contains custom lists  which have created programmatically . Both of these sub sites also contains current navigation ( which contain different navigation link) created programmatically .Every thing is working fine but problem occurs when I implement variation   on my portal ,my source site perfectly propagated site content like web parts but did not propagate  custom  navigations  and custom list. how can I propagate my custom navigations and custom list.

I've done a great deal of work on expanding Variations functionality over the past few years. Custom lists and custom navigation are not going to propagate without custom code.

As an example I wrote this some years ago;

http://the-north.com/sharepoint/post/Propagating-Document-Library-Items-In-MOSS-Variations-(in-the-same-way-as-Pages)

It's not fantastic code, I've learned a lot about the Variations API since then but it shows the directions you need to explore.