I'm a big fan of the "Choose Your Move" magazine articles. I find that they are a fun exercise, both as a player and a coach. The only difficulty is having someone to do it with. I know that they are intended to be done as a solo exercise, but the mechanics of covering up future moves can be a little annoying, and difficult to always get right.
Even if you have a partner, one person often feels left out, as the solver seems to have all the fun. But there is a related exercise that can involve both players.
The following coaching technique was shown to me by Julian Mott, who ran the first junior chess club that I joined as a teenager.
Simply play a normal game of chess, either without clocks, or with a reasonably generous time lime (G/20 or above). When you write down your move, also write down what you expect your opponents reply to be as well. Both of you can do this for every move of the game. At the end you can compare who got the most predictions right.
For experienced players this just may be a function of knowing the other persons game. But for newer players it helps build up the discipline to anticipate an opponents reply to your move. Too many beginners go for the "hit and hope" strategy, rather than the "if I go here, then he goes there" approach. By using this method, hopefully new players will build a more all-round understanding of the game at an earlier age.