Although it may not be a solution you're in search of, but from the requirements you have, it seems like a custom LayoutManager may be able to achieve what you are after. By designing and assigning a custom Layout Manager which allows line breaks to a Container (such as Panel), it should be possible to have a Panel which allows line breaks.
The Laying Out Components Within a Container article from The Java Tutorials will provide general information on how Layout Managers work in Java, and in particular, the Creating a Custom Layout Manager will provide information on how to make a custom Layout Manager to apply to an Container.
The behavior of the FlowLayout (the default Layout Manager for Panel) seems fairly close to the behavior you may be after. Adding functionality to line break seems like the missing piece.
Suggestion: Perhaps the custom Layout Manager can have the ability to add a line break by having a Component that represents a line break, which can be added to a Container by using the add() method.
For example, have a class constant Component in the custom Layout Manager, such as (a hypothetical) LineBreakLayout.LINE_BREAK, and adding that to the Container can tell the custom layout manager to move to the next line. Perhaps an implementation can be like:
Panel p = new Panel(new LineBreakLayout());
p.add(new Label("First Line"));
p.add(LineBreakLayout.LINE_BREAK);
p.add(new Label("Second Line"));
The above hypothetical LineBreakLayout will then render the first Label in one line and the second Label in the second line.