Unfortunately, I don't think that's something I have any control over on my end. I haven't used LJ in a few years, but as I recall, they restrict a lot of formatting in their comment fields. If they don't allow tables in comments, I'm not sure there is an easy workaround.

If other tables are showing up fine, and it's only the ones from the bingo generator which won't work, my guess would be that it's an issue with the inline CSS; I know LJ's made changes in the past which have been pretty hostile to inline CSS. In that case, I'd try removing the entire style="" attribute from the tags, so you just have plain <td> tags and a plain <table> tag.

Let me know if that helps at all!