What's the best way to get a charcoal taste on a propane grill?

From what I see you have 2 options.

1. you can Add liquid smoke to your bbq sauce you use (if you use). Warning, a little bit is alot.
2. you could create a 'smoke packet' soak a handful of hickey wood chips, wrap in aluminum foil and poke some holes. Place this packet underneath the grill, once you get some smoke coming out, start cooking your meat

Whether or not charcoal tastes different/better is actually a bit of a debate. I've been a propane griller for years and now I use charcoal not for the taste, but because frankly, I like to play with fire. But lets assume that there is a taste difference, identify where the differences comes from, and how to address them:

1. The smoke from charcoal. This is (if you've been using natural lump charcoal) pretty much just wood smoke. If you've been using briquettes you'll also get the smoke of the filler and such, but generally this isn't desirable and we don't want to replicate it. For smoke on a gas grill - you can use something like this smoker box. Fill it with wood chips and place it over a burner, it should start smoking.

2. Vapor from the food drippings hitting the coals, and rising back up to flavor the food. This used to be a big advantage to charcoal, but its largely minimized by new gas grills with 'vapor bars'. As long as your grill has one of these, you're in luck. Otherwise, there's not a good, safe way to replicate it - but odds are you have it. Its a long bar usually running the length of burners.

3. Lighter fluid taste. Another undesirable flavor if you're doing a particular (and not good IMO) kind of charcoal grilling. Frankly, its not one you're likely to miss.

Those are the main tastes and how to replicate them. Nowadays the biggest is definitely #1, but it only matters if you doing foods that cook for a significant length of time or are especially 'porous'. If you're doing hot dogs and chicken breasts, I wouldn't bother if smoke. If you're doing burgers - maybe/probably. If you're doing thick steaks, thick pork chops, a whole chicken, or anything that's going on awhile, then creating some smoke is definitely worth it. ("Liquid smoke" definitely doesn't taste like the real thing.)

I think that you will have a hard time getting charcoal flavor without charcoal. Smoked flavor, however, is obtainable. If you have an outside grill, fill a small disposable aluminum pan with water-soaked wood chips (hickory or apple wood are nice), and stick it in your grill with the meat with the lid down.

If you're talking about a gas grill that's on the range top of a kitchen appliance, this is probably a bad idea (smoke alarms, fire department...). However: America's Test Kitchen did a wonderful episode of smoked/barbecued ribs achieved in the oven. Can't find a link that's not behind a pay-wall right now, but I believe the method involved a roasting pan with a rack set in it, soaked wood chips, and covering the whole contraption with foil in an oven for many hours. Maybe other posters can help out my foggy memory.

While I like the "Smoke Box" approach that @rfusca offers you can accomplish the same effect with an cheap/disposable aluminum tray (like those pot pies come in) and a few wood chips, it really doesn't take much smoke to get the flavor into your meats. Just place the tray on the grill slightly away from the meats and let it get to smoking before you put you steaks/burgers on, and keep the lid shut.

Another option is to use "Liquid Smoke". This must be done carefully and in small doses as a little goes a long way. You will get the best results out of mixing Liquid Smoke with something. For steaks I like to mix about a teaspoon with a stick of softened butter (along with garlic, rosemary, oregano if you like...) whip it up and then chill it. While grilling, after you have turned the steak add about a tablespoon of the butter. As it melts it will impart a subtle smokey goodness to your steak. (also works well with chicken)

For burgers mixing a tablespoon of the butter mixture in to the patty when you are forming it works well. However, I like to mix a little Liquid Smoke with some BBQ sauce and work that into the raw ground beef and then form that to patties and grill normally.

On an episode of Good Eats Alton Brown demonstrated how to make liquid smoke. Something which every serious griller should try, ONCE. ;)

Avoid the liquid smoke stuff. It tastes horrible in my opinion. I bought a small "smoke box" at Lowes. It's just a cast iron box with slits in the lid. By some wood chips, I like apple wood, and soak them in water for a while. Then put the smoke box under the grill but over the flame. It works well.

How about a seasoning with a smoked salt?

Yep, you can. The first step would be to buy some lava rocks or similar additive to your gas grill (if it's cheap). This will even out the flames and get you a better cooking situation, more similar to the charcoal barbecue.

Second would be throwing some wood on the fire; you can do this in an aluminum foil box, with a metal 'smoking box', or just throwing some wood on the grill as you prefer.

If you do that, use hardwood only; probably it's best to start by buying a bag of hardwood chips for grilling. Softwood produces nasty smoke which tastes terrible.

You can even put a lump of charcoal on the grill. I like to use a tuna can that's been well washed as a tray for it.

Have a bucket of water handy for dousing.

Get some lava rocks or something like that. Put them on the grate under your cooking grate. Then put a few apple sticks or what ever you would like on top of the rocks, let it heat then put your food on the cooking surface. Close and enjoy ;-)

I have put a few charcoal briquettes in my propane grill on occasion, and have used the smoker box that Lowes sells. Mix wood chips with charcoal crushed seems to work better to put in about 15 minutes before put meat on to get good smoke going.

You can use smoke flavoured BBQ sauce to either marinate your meat, or applying it while it is on the grill.

I have been grilling tri tip for a couple of years and finally got the timing down perfect. I wanted to kick it up a notch tonight. I don't have any wood chips, but I did have some briquettes with mesquite in them. I put the briquettes in the foil pouch over direct heat while my meat cooked over indirect heat. The best I've made so far. Next time I will try to make the holes in the pouch bigger to allow for more oxygen flow and more smoke.

Edit: forgot to include that I have been grilling on a propane grill for years.

I don't know whether they banded it or you just don't see it anymore but they do have charcoal seasoning maybe at a health food store.

Search for Calhouns Charcoal Grill Seasoning out of Tennessee is excellent. Ran into it by accident. And it can be bought online! This is not to negate other suggestions here. I would say use Calhouns in ADDITION to some of the fine tips already mentioned.