Theoretically, You can convert a fire pit table from propane to natural gas.  However, we "highly recommend" that you Hire a professionally licensed mechanical contractor to convert your fire pit from a propane tank to natural gas.
Propane and Natural gas have different gas densities. In addition, natural gas as a fuel source requires specialty-sized orifices, fittings, and of course, a natural gas hose, and all of these are critically important to get done correctly and, in our opinion, professionally.