None of the sentences by the OP are "correct" for several reasons.
- As JavaLatte's answer explains, the definite article, the, is required before court, and I don't see any justification for capitalising it either. The word court is not a proper noun and unless the actual tribunal building is called "Court", it should not have a capital letter. Thus if we operate the necessary changes we are left with this
- (a) Last year, the court had convicted him for murder.
- (b) Last year, the court convicted him for murder.
- Next, the biggest obstacle in my view is not which tense is used but the preposition "for". Again, this is also mentioned in JavaLatte's answer.
Prepositions are awkward little words, sometimes more that one preposition can fit but carry a different nuance in meaning, e.g. think about and think of, other times there is no difference in meaning but much depends on your dialect, e.g. at the weekend and on the weekend. But in the case of convict the preposition used by native speakers is, without doubt, of. This website claims that convicted of is used 91% of the times whereas convicted for is only used in 5% of the cases.
With The Grammar Fixed…
- (a) Last year, the court had convicted him of murder. [PAST PERFECT]
- (b) Last year, the court convicted him of murder. [SIMPLE PAST]
Now, both sentences are grammatical and respect the norms of spelling and punctuation. This is where I differ from JavaLatte's answer and I agree with Colin Fine's. Without further context, it is not possible to say which sentence is preferable, a bare sentence, as long as it is grammatical cannot be "wrong".
The Present Perfect
- The OP believes that a timeline cannot be used with the perfect aspect. That is not entirely accurate. It is the Present Perfect that is not normally used with an expression of time
- (c) WRONG: Last year, the court has convicted him of murder
The sentence is in nonstandard English or ungrammatical (depending on one's point of view), the Present Perfect is used when our focus is not on the time the action occurred; e.g., “The court has convicted him” and when the speaker is more interested in the results felt in the present e.g. the assassin has been found guilty of murder and will be sentenced. He cannot harm anyone now.
- (c) CORRECT: The court has convicted him of murder. (Now, he is in jail) [PRESENT PERFECT]