what kind of plants can you put in a rockery which is situated under trees

Gizmo - sorry if your rockery is such that the plants will get no sun then I personally don't know of any alpine plants that will grow there, especially as the trees will be taking all the nourishment from the soil. You could try periwinkle and celandines but even they will struggle!

Try Campanula poscharskyana. and Dwarf Junipers. .Spring bulbs and Euonymus Emerald and Gold. Not real Alpines but give a bit of colour. Solomon's Seal and Lily of the Valley also.

Ferns if it's damp, too.