Add items to a jQuery Accordion with jquery

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