I recently was given a propane grill that is a lot nicer than my charcoal grill, however my family really likes the cooking and taste of a charcoal grill. I hear the propane grill tastes a lot different. Is there something specific I can do to get a taste similar to a charcoal grill, while using the benefits of my newer, nicer, larger, propane grill? 
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:   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. 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. 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.) 