A couple of things that are useful in COIN that have no real place in conventional operations:
1- security detachments for commanders: every commander needs the ability to move around the battlefield, this likely means 3 or 4 vehicles with crews (so 12-15 personnel). In conventional operations, this requirement manifests very differently, and you send a complete sub-unit when the security situation requires.
2- human intelligence gathering capability. In COIN, when you are securing a relatively fixed area, HUMINT at a very low level is very important. In conventional operations, other than initial review of prisoners, you're not likely to have the time at the battalion/company level to build a network of informants.
3- platoon/company command post crews, particularly intelligence and signal support. In conventional operations, this is the platoon or company commander's vehicle crew, with maybe a communication specialist. In COIN, when you operate from a fixed site and do much deeper analysis of the human terrain of an area, you require the capability to do this analysis, and maintain significantly more communications equipment at lower levels.
4- requirement for indirect fires is significantly reduced. Insurgents lack the capability to mass large forces that justify the expenditure of large scale indirect fires- we never had a target in Afghanistan where I needed another battery, and generally 2 guns was sufficient. You can either break your firing units down to distribute the coverage, or re-role your artillerymen to provide maneuver/security forces. If you're designing only for COIN, you can just create those maneuver/security forces to start with.
5- the structure of engineering support is very different- COIN is much more focused on route clearance of fixed and routinely used routes, while conventional operations are much more focused on the creation (and breaching) of defensive obstacles.
I'm sure that there are move, but those are what comes to mind quickly.