Not really. You can buy little cast iron boxes you put wood chips in, and put them inside your gas grill. There's stuff called "liquid smoke" but I wouldn't put that poison on any food I'd want to eat.

Instead you might want to exploit the clean heat characteristics of your gas grill, and let the natural flavors of the meat and spices come out.

I find that Pappy's Choice Seasoning (I found it at Costco) give a great flavor to poultry, and good old Mrs. Dash works great on beef.

Finally, generally speaking, meat that is smoked or cooked over charcoal has more carcinogens than meat cooked with gas or electricity. So that smoke taste you miss might not be all that good for you anyway. (I like a light smoke taste anyway, myself, too, but life is generally a compromise).

You can also put a little lighter fluid in your marinade...ok, that was just a joke. I second spambdamn_rich on trying a wood chip smoker, and there is good advice in these forums on how to make those work effectively (adding water, covering with foil, etc.) I would hope the smoked wood would be superior to the flavor of charcoal, but maybe it is a preference issue.

I was wondering how easy, difficult, or expensive it is to convert a Weber Genesis grill I inherited from natural gas source to Liquified Propane?

Bcar,

You should contact Weber to see if they sell a conversion kit for this. You will probably need burner jets with smaller orifices and a regulator that can handle the high pressure of LP. Do not attempt to do this without the proper mfg kit. If you run propane through a burner designed and jetted for NG then you might get a huge flame, a meltdown, or worse.