Does anyone make flip down scope covers for the CompM4s? Butler Creek maybe? Is it even possible with this scope?

The M4 uses the same size Flip-up Covers as the M3.  
The OEM Flip-ups from Aimpoint are made by Butler Creek.  
The only issue with using them is the front one will have to be removed when you replace the battery, but having to do this every 8 years shouldn't be an issue.
Sorry don't know the size Butler Creek you need.

Brownells has the OEM Flip-ups:

Brownells
Front #100-003-612  /  Rear #100-003-616

Well after much digging I found the info and want to share it in case someone else has this same issue:

MilitaryMorons website says that the Aimpoint scope covers 12223 and 12224 (one each) fit on the CompM4s.

http://www.militarymorons.com/weapons/ar.optics.html#m4

I bought them from OpticsPlanet (unfortunately, they are $17 each, pretty pricey for a piece of plastic if you ask me).
The front cover fit very snuggly and was difficult to put on. The rear one went on easy. Both covers have a ridge on the inside that fits into a groove on the optic and helps hold the cover in place.

But overall a far superior solution than the rubber doo-dad that ships with the optic. Too bad after spending over $600, a decent set of covers couldn't be included.

There are also flip-up clear plastic covers available, which are particularly nice and I believe similarly priced.

Update:  it is necessary to remove the front flip up cover in order to change the battery. Very annoying, considering how difficult it is to get the cover off and back on again. Luckly the CompM4s has such as long battery life.