You mean conversations of your own or of other members ?
If you want to search yours, they are here http://forum.canta-per-me.net/conversations/
while you cant search the ones of other members since they are private
there is a small search option. In the conversations window I posted above, at the bottom of the window there's a link "conversations display options" where you can sort your conversation or search based on username of the one you conversated with. Other than that you should ask Sudrien ^^