A. Spain’s governing coalition has come under strain as it pushes its painful austerity measures, and it must now enforce agreed-upon measures, laying off 4,000 civil servants by the end of August, which will push forward a stalled project to privatize state assets.

which should always be followed by a comma and should refer to the noun before comma. Here "which" is incorrectly referring to August.

C. Spain’s governing coalition, which has come under strain as it pushes its painful austerity measures, must now enforce agreed-upon measures, laying off 4,000 civil servants by the end of August and pushing forward a stalled project to privatize state assets.

Here "which" correctly refers to Spain’s governing coalition. Moreover laying off 4,000 civil servants and pushing forward a stalled project are parallel in structure. And C is the intended meaning of the sentence whereas A distorts the meaning

Only (C) has a coherent and logical structure: “The coalition, which has been facing this, must now enforce measures, laying off these people and pushing forward this project” The “which” clause in the middle is properly used to modify the coalition and the two “-ing” phrases at the end are parallel and properly modify the coalition and how it must enforce the measures. In (A), the “which” clause has nothing to logically modify and is thus incorrect. In (B), the phrase “pushing forward a stalled project to privatize state assets” cannot be logically linked to the verb clause “lay off 4,000 civil servants” Laying off 4,000 civil servants has nothing to do with pushing forward a stalled project to privatize state assets. Those must be two separate modifying phrases relating to how the coalition must enforce the measures. In (D), the subject “Spain’s governing coalition” has no verb to follow it anywhere in the sentence. (E) suffers from the same flaw as (B) and the semicolon disconnects two things that should be linked in one sentence.

Thanks a lot!

Only C has a coherent and logical structure.

Only C has a structure that makes sense.