I just updated to LDD to 4.3.9 today and I can't find the 2 by 2 turntable pieces. What section are they under now?
You'll find them in the hinge parts category (next to minifig one) under the name "Turn Plate 2x2", number 3679 / 3680. Brickset uses LEGO names for parts, this can help finding them in LDD
I agree with SMS von der Tann... I'd upgrade LDD to 4.3.9 and the turn plates 2x2 ARE NOT in any category anymore (I seek it everywhere more than twice). My solution was to save a 2x2 turn plate, from another LDD model I made before upgrading, to the templates and then re-use it when I need.
If you temporary change your theme to the extended LDD, the turntables are still in the hinge section, this way you can paste them into your build and color them, after that you can change back to the normal theme of LDD