A mourner (avel) is permitted to say she'hecheyanu for himself but should not say she'hecheyanu if required for the congregation.  An avel should say she'hecheyanu on:

• Eating a “new” fruit.
• Wearing a new garment.
• Lighting Chanuka candles at home for the first time that year.

 An avel should not do the following, since he should not say she'hecheyanu unless it is necessary:

• Light Chanuka candles in synagogue.
• Read the megila.
• Blow shofar on Rosh Hashana.