First, the jacket doesn’t need to be a part of the same hierarchy as the joints. It can be anywhere in the scene hierarchy outside the joints hierarchy.
In the Character menu, select the “Skin” deformer and make that a child of the jacket mesh object.
Select the “Include” tab of the Skin deformer, change the mode to “Include” and drag the jacket mesh object into the list.
Now select the jacket mesh object and in the tags menu find the “Weight” tag (under rigging in r21 and I think Character under r20-).
Now that the Weight tag is added to the mesh, lock the attributes manager, middle-mouse-click the root of the joints hierarchy (which will select all children as well) OR select the root and from the objects manager menu bar goto: Edit > Select Children.
Drag that selection into the joints list of the Weight tag (that was locked in view in the Attributes manager)
Now you can unlock the Attributes manager.
Select the jacket mesh object.
open the weight manager: Character menu > Manager > Weight Manager
Paint weights or use the Auto Weight feature.
To Paint weights, switch to the Paint Tool: Tools menu > Paint Tool
Switch to points mode and adjust your paint settings in the Weight manager on the Commands Tab.
Select specific joints to assign weights to on the Joints tab of the Weight Manager (you can keep both tabs open by click-dragging across them or shift-clicking them).
Have fun painting!