Many of the suggestions unfortunately do not work for all Markdown viewers/editors, for instance, the popular Markdown Viewer Chrome extension, but they do work with iA Writer.
What does seem to work across both of these popular programs (and might work for your particular application) is to use HTML comment blocks ('<!-- -->'):
Like some of the earlier suggestions stated, this does add an empty header row in your Markdown viewer/editor. In iA Writer, it's aesthetically small enough that it doesn't get in my way too much.
Empty headers in PHP Parsedown produce tables with empty headers that are usually invisible (depending on your CSS) and so look like headerless tables.
If you don't mind wasting a line by leaving it empty, consider the following hack (it is a hack, and use this only if you don't like adding any additional plugins).