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Any wooden or mostly wooden item (such as a bow or spear) made from darkwood is considered a masterwork item and weighs only half as much as a normal wooden item of that type. Items not normally made of wood or only partially of wood (such as a battleaxe or a mace) either cannot be made from darkwood or do not gain any special benefit from being made of darkwood.
So... no.

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I was under the impression that morningstars, like maces, had a steel (or at least steel-cored) haft - but on reflection I'm not sure it's specified either way. (The maces, at least, are specified in the Sunder section of the rules.)
But either way, I'd infer from the battle-axe being out that the morningstar is out too. (This makes me wonder which pole arms are over the line.)