Many stampers own the Janome Sew Mini for sewing on cards. It is a little more expensive than $50, but you can get it on Amazon for $64. It is a real sewing machine, and not a toy. You can also use it for sewing on fabric. Here is a link:
Amazon.com: Janome Beach Sew Mini Sewing Machine
As an alternative to sewing on your cards, the stitched dies are very popular right now. Lots of companies make them. Just google and look.
Or, you could use your paper piercer to make holes in your cards, and use a pen to connect them to mimic the look of stitches.