There are 12 Bl/R Troops in the game thus far, and they cover the board in types, and turns out one is a construct.
There are only 9 G/Br Troops in the game, and Archon Statue is Divine…even though it’s a stone carving…constructed by man.
Just make a card that’s a robot made with wood and BAM! G/Br Construct, at your service. Eazy, peezy, Covergirl.
I also understand that most Troop Types tend to stick to a main color (Fey/Elf/Wildfolk stick with G/Y, Undead usually have P, Giants and Constructs usually having Br), but the also do some left-field stuff occasionally, and there’s no harm in having a couple Troops of a certain type break the mold (like Borer: it’s R/Bl, and Bl seems a bit odd for a Construct, right? But it happened).
So if you have, say, only one G/Br Construct ever made…that would be perfect. Make it unique and not have a very ‘construct-like ability’ and then people will build what they choose with it.