What lab would demonstrate the law of conservation of matter?

Just show that matter can change form, but not be created or destroyed.  So some examples:

Take liquid water, weigh how much it is.  Then freeze it so it's solid ice and weigh it again- it'll be the same.  Now the matter has changed form, but there's still exactly the same amount.  The volume and shape may not be the same, but the amount of "stuff" is the same.  You can even repeat the process of melting and freezing several times and weigh after each time, and show that the matter is not going anywhere.

I'm not sure if you want to go down this route, but create a chemical reaction.  Have two components and weigh them.  Combine them so that they form some new compound, and prove again that the weight is the same even though a chemical change has taken place.  You can probably find examples of simple and safe chemical reactions by doing a quick google search.

Those are just two quick ideas, but basically, all you're proving is what I said before- matter can change form and look different, but it'll always be the same amount.  

Now just to be technically correct- and this is something you won't have to worry about for a long time- matter and energy are the same thing and one can be converted to the other.  So really, matter can be destroyed, but only if you create an equal amount of energy.  Again, just saying that for completeness- for now, just assume that matter cannot be created or destroyed.

Hope this helps