I believe you could do it like this:
- Select the object to stroke on your art board
- Open the "Appearance" panel in "Window"drop down menu
- Add an additional fill layer to the object in the appearance panel. (Just a square icon in the footer)
(While in the panel, make sure you have the lower layer fill selected)
- Fill it with the color you want the stroke on the one side of the object. (If done correctly you actually wont see anything happen. Don't worry)
- With the lower fill layer in the appearance panel still selected, click the FX drop down on the appearance panel.
- Select "Distort and Transform>Transform"
- In the Transform dialogue box, click on "Preview" in the lower right, so you can see what you are doing.
- Then just play with the horizontal/vertical move sliders (depending on which side of your object you want your stroke) until you have what looks like a stroke on one side of your object.
- When you are happy, just drag the whole object from the art board into your style panel.
That should do it. Granted, it is not a true stroke...but it should give the effect you want provided the top fill is not a transparency.
Since you want to add a custom brush, you could probably add a stroke to the underlying fill with the desired brush and play around with the offset path in the "Paths" drop down FX menu. Either way, I am certain your answer lies in the under appreciated appearance panel.
Hope this helps.
(I don't have Illustrator on this computer, so this is just from memory, forgive me if I missed something.)