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I am looking for a single verb that means "to declare (one) a liar" or "to accuse (one) of being a liar" - a verb that can take an agent. For example, I could replace "was declared a lair" in the following sentence with the passive form of this verb:

She gave a convincing testimony, but was declared a liar by the prosecutor.

It needs to have a negative connotation, like the verb "to allege". In other words, the agent is falsely accusing the subject of being a liar.

Any ideas?

A good use for the word traduce!

"She gave a convincing testimony, but was traduced a liar by the
prosecutor." (Past Indefinite, Passive Voice)

traduce Vocabulary.com

to expose to contempt; to bring discredit upon; to dishonour, to disgrace; to malign

and OED:

To pervert, corrupt, misrepresent, falsify; to turn into something bad

As in:

Instead, my reputation was traduced, my story distorted, my
credibility made hostage to smears. The Guardian Apr 19, 2018

and

The senator believed he been traduced by those who seized upon his
controversial comment. Economist May 13, 2018

Synonyms: badmouth, drag through the mud, malign

If the accusation is not necessarily false, you could use label, or for a more strongly negative connotation, brand or denounce.

She gave a convincing testimony, but was denounced as/branded a liar by the prosecutor.

Otherwise, there are a host of words meaning "to falsely accuse" which may be appropriate here.

Slander, defame, calumniate, asperse, malign, smear in addition to traduce mentioned elsewhere.

She gave a convincing testimony, but was maligned/calumniated as a liar by the prosecutor.

Of these, traduce, asperse and calumniate are less likely to be understood.

Here's an interesting comparison of a number of these words from Merriam Webster:

malign, traduce, asperse, vilify, calumniate, defame, slander mean to injure by speaking ill of. Malign suggests specific and often subtle misrepresentation but may not always imply deliberate lying: the most maligned monarch in British history. Traduce stresses the resulting ignominy and distress to the victim: so traduced the governor that he was driven from office. Asperse implies continued attack on a reputation often by indirect or insinuated detraction: both candidates aspersed the other's motives. Vilify implies attempting to destroy a reputation by open and direct abuse: no criminal was more vilified in the press. Calumniate imputes malice to the speaker and falsity to the assertions: falsely calumniated as a traitor. Defame stresses the actual loss of or injury to one's good name: sued them for defaming her reputation. Slander stresses the suffering of the victim: town gossips slandered their good name.

refute

"She gave a convincing testimony, which was refuted by the prosecutor."

refute

VERB
1 Prove (a statement or theory) to be wrong or false; disprove.
‘these claims have not been convincingly refuted’
Oxford Dictionaries