I've not made a weld bead before and could use some help. The
image below shows my assembly. The current design calls for the
entire cone area to be filled with weld. I tried using a V-groove
weld but it fails giving me "Selected faces from different
components must shard at least one coincident edge for this weld
bead operation". Do the Contacting faces have to have one
coincident edge? I wouldn't think so but I'm not sure. I assumed
that having the stopping faces coincident mated would satisfy the
coincident edge requirement.
The 4 faces of the cones are my contact faces
The top and bottom of the green plate and the top and cone end of the red plate are my stopping faces.
The 4 faces of the cones are my contact faces
The top and bottom of the green plate and the top and cone end of the red plate are my stopping faces.

It appears that there is clearance between the faces you're trying to weld. I can't speak for the latest versions, as I stopped upgrading at 2007, but the weld bead feature has never been able to fill gaps, so unless there is a continuous line of contact between the faces, you will be unable to add a weld bead. Seems odd, I know, because filling gaps is the very purpose of welding in many cases. I would love to be able to add welds to my models, but the function so rarely works that I don't waste my time trying to use it any more. Sorry for the bad news.