I suppose you should create new uv-mapping for a capsule primitive.
First of all, you need to make a mesh seam (cut) in the bottom of it (the area that is barely seen in game), like on the image below. Note, it you can't reach some vertex by hovering it, hold mouse still and tap CTRL key several times until needed vertex is highlighted.
Then edit UV on objects level by generating new UV unwrap (and make sure to toggle off continuous mesh surface, so mesh seams are respected)
then edit/arrange uv charts in uv-mapper view. On the image below there are three charts/fragments generated: two caps and one for body: