You need two paths for the text: one for the upper text, one for the lower.
I don't understand your problem with the stroke - just apply a stroke.
Presuming you are creating a circle, then using the Path Type Tool to make the top text, and wishing to have a bottom text as well as getting some colour back into the circle, you may:
1) Select the whole thing and Object>Transform>Rotate by 180 degrees,
2) Drag the wrong bottom text across the circle so it flips inside the circle but is upwards, then use Character>Baseline Shift to get it under the circle if desired,
3) Direct Select the (copy) circle and give it the desired Stroke colour.
Text paths loose their color and you have to reassign it. Select the path by clicking it with the white arrow and assign a color. You may need to use the outline view to see the path.
For the text you have to make a copy of the text path and then change the word and orientation. You can't have different orientations on the same path.
edit: haha three people replying at the same time
You can do it in a number of ways.
One of them is to:
1) Create the circle and cut it at the sides, and reflect the bottom half,
2) Use the Path Type Tool on each half, and use the Baseline Shift to drag the bottom text down if desired.
The reflecting makes the bottom type upright from the start.
Edit: Hi Monika and Emil.