I think I may have found a solution to this issue as it is one I have had as well.
In the Layers drop down menu you will find Layer Effects.
First select the layer you want to change the colour of.
Then click on Layer Effects in Layers drop down menu from the main navigation menu.
Now select Colour Overlay.
You might have to click back the layer to have the colour options show up, but you will find that you can change the Blend Mode, Opacity and Colour.
If you click on the colour swatch other options and the Eyedropper will become visible.
Then you can use the Eye Dropper by holding down the option key at the same time as dragging the eye dropper.
I agree it would be better if this was made more obvious.
It would also be beneficial to be able to key in the colour you want, but if you use a third party app like Color Picker you can get around it easily with the Eye Dropper
Some times its just knowing where the tools are in the software.
I took a screen shot so you can see for yourself. (see below)