I haven't tested it, but this should probably work:
Say that you have your accordion with id #accordion
$('#accordion').append('<h3><a href="#">New Paragraph</a></h3><div><p>New data</p></div>')
.accordion('destroy').accordion();
Basically, just destroy and re-create the accordion.
UPDATE:
Since this answer was written a refresh() method has been added to the accordion widget. It can be invoked by calling:
$( ".selector" ).accordion( "refresh" );
You can read more about this method here
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