Grammatically it sort of works. But there is a word definition mismatch. A coalition is two or more parties joining together, most commonly government parties. This is the definition in native speakers mind a government coalition, so the sentences is confusing. analysing it by dictionary definition and the idea of a coalition that is firmly entrenched in native speakers minds. Your sentence reads. "The citizens have given approval to the government, by the government". You seem to have inadvertently described some people opinion of "Brexit" "The citizens have elected a coalition government, there being no overall approval for any party"

Original: “The citizens have given countenance to the government by coalition.” If we are determined to maintain your original wording, I would suggest to reword as "The coalition of citizens has countenanced the government." or reducing passive voice with “The citizens' coalition has countenanced the government." Including "have given" is incorrect as the word "countenance" in this context is a verb (to lend or give support). Another example sentence containing both words could read: "After a series of successful negotiations, the coalition of activists voted to countenance the opposition's proposed amendment." Edit: Changed "have" to "has." The noun is coalition, which is singular. My apologies.

First of all, I'm just curious why you want to? I don't think your example works because the preposition "by" isn't really used with coalition like that. I suggest: 1. The coalition of citizens have given countenance to the government. 2. The citizens have given countenance to the government as a coalition.