bump

is the conversion meant to be temporary and casual (like for games)? would it be a problem if you just placed a square on top of a round table for just the day? you could use a rubber shelf liner to keep it from sliding around.

or if you don't want it to look like two tabletops stacked up, you could buy a base with a removable square or round top, and then have a separate top cut to size. I've only seen glass tables with removable tops though.

like this one from crate and barrel:

if you want it to be all wood, you might need to find a custom furniture builder.

Years ago I saw a picture of a table that was square. It had hinged side pieces on all four sides, which when raised made the table round. I think I would talk to a local furniture maker to see if a purchased square table could be outfitted with hinged side pieces. If the table was just right ?? then it should not be too hard to do. Otherwise, At one time I had a round table and wanted it big enough for guests, so put a piece of plywood on it to make it oblong. With a pretty tablecloth it looked fine. I think you could do just the opposite (like someone mentioned) by putting something round on top of your square table.

Winners Only Zahara DZH4260 Traditional Round Dining Table with Granite Lazy Susan | Reeds Furniture | Table - Dining (formal) Like this one!