I don't think they interact at all.
Ironwood is a magical substance created by druids from normal wood. While remaining natural wood in almost every way, ironwood is as strong, heavy, and resistant to fire as steel. Spells that affect metal or iron do not function on ironwood. Spells that affect wood do affect ironwood, although ironwood does not burn. Using this spell with wood shape or a wood-related Craft check, you can fashion wooden items that function as steel items. Thus, wooden plate armor and wooden swords can be created that are as durable as their normal steel counterparts. These items are freely usable by druids.
While ironwood is made from normal wood, darkwood isn't normal wood. I don't think a darkwood item is a valid choice for the ironwood spell.
However, if you could cast ironwood on a darkwood item, the weight would indeed go up. The item is no longer darkwood, but is now ironwood. Ironwood is as heavy as steel.
It... it grows. As trees. How is it not normal wood? Is oak normal? Redwood, Ash, Ebony, Elm? Yew?
The description indicates it isn't normal wood.
Darkwood: This rare magic wood is as hard as normal wood but very light.
It is rare, magical wood.
Normal wood (or normal anything, really) doesn't have special rules. Oak, redwood, ash, ebony, elm, and yew would all be normal wood. As far as the rules would be concerned, they are all the same.
Darkwood isn't normal wood - it is magical and weighs a lot less.
Greenwood isn't normal wood - objects made from it can heal themselves.
Whipwood isn't normal wood - it is a crafted material.
Wyroot isn't normal wood - it can suck out life force.
All those woods grow as trees. (Edit: Well, except greenwood. That is taken from a tree animated by a treant which may have been a normal tree at one point, but isn't any longer.) That doesn't mean they are all normal wood.
There is a difference between "normal" and "natural". All those trees are natural, but not all of them are normal. Some of them are special.
Hmmn... it is specifically magical? So darkwood objects lose their properties in an antimagic zone? Can they be dispelled? What is their caster level? So many implications! Do they get saving throws while unattended?
Not everything that is magical loses their properties in an anti-magic area. For example, contructs although clearly magical, can function just fine.
Darkwood is a little bit like a construct in that way, the 'magic' was integral to making it what it is, but doesn't actively require magic.
Frankly though, if you had a sword made of darkwood, and cast ironwood on it, I doubt it would make that much of a difference to let it keep the halved weight property of darkwood.
Frankly though, if you had a sword made of darkwood, and cast ironwood on it, I doubt it would make that much of a difference to let it keep the halved weight property of darkwood.
Whether or not it makes a difference is beside the point. In the Rules Questions forum, what the rules say goes.
Personally, I have no problems with theironwood spell only increasing the durability of an object without changing the weight. But the rules don't care about my personal opinion.
Even if you decide that Darkwood is a valid target for the Ironwood spell, it is pretty clear that Ironwood as a transmutation spell, changes the wood from what it was into something different, so it wouldn't be Darkwood at all any more, it is just Ironwood.
While remaining natural wood in almost every way, ironwood is as strong, heavy, and resistant to fire as steel.
Darkironwood, if it existed, would offer no benefit over ironwood other than the lower armor check penalty for a shield--and that's debatable if one concludes that the lower penalty is due to the diminished weight.
But darkwood is magic wood, which is not normal wood. Ergo, this is moot anyway.