The Ares Alpha has an underbarrel Grenade Launcher so it can't actually take under mounted recoil compensation (Relevant Text from Arsenal pg. 153: The underbarrel weapon modification cannot be combined with other underbarrel modifications or accessories that reduce recoil).
That said, you can still get it up to 8 (Heavy Barrel 1 (3 slots), Personalized Grip 1 (1 slot)) Gas Vent III Accessory 3, Sling Accessory 1, Special Chambering* 2. This set up leaves you with 2 slots left on the weapon as well as a top mount and an under mount. If you have a STR of 6+ it will take you RC up to 9 and if you have a STR of 10+ you'll have a full 10 pts. **
* The Ares Alpha has two free points of RC from its special chambering design.
** The Recoil Compensation granted by Heavy Barrel only applies to Full Bursts.
If you don't mind being obvious, you can take an AK-97. Put a Gas Vent III and Sling Accessory on it for 4 RC. Give it the Personalized Grip (1 Slot) modification for 1 RC. This gives you 5 RC (enough for 2 short bursts). Now buy a Gyro Stabilization Harness to wear for those heavy assault runs and bump that up to 11 RC*.
* The Gyro Stabilization Harness negates up to 6 pts of Recoil and Movement penalties, so while 11 seems wasteful, it can come in handy to go full blown like this.
**If allowed to use Gun Haven/Heaven, the AK-112 and HK G-36 are Vintage (causing some issues with electronic mods and accessories), but seem to come with one point of free RC. The QBZ-14 likewise seems to come with one free point of RC.