When is calling a person a liar not defamatory?

Yes. The leading U.S. Supreme Court case is Milkovich v. Lorain Journal Co., 497 U.S. 1 (1990), which held the opposite of a blanket “liar” privilege: calling someone a liar can be actionable if, in context, it implies a provably false assertion of fact. The Court specifically said that a statement like “In my opinion John Jones is a liar” may imply factual assertions and therefore is not automatically protected. Milkovich v. Lorain Journal Co., 497 U.S. 1 (1990)

If you need a case holding that “liar” was not defamatory because the context made it rhetorical hyperbole or nonfactual opinion, the best authority in the materials provided is Greenbelt Coop. Publ’g Ass’n v. Bresler, 398 U.S. 6 (1970). There, the Court held that describing a developer’s negotiating position as “blackmail” was not actionable because, in context, “even the most careless reader must have perceived” it as “rhetorical hyperbole.” Greenbelt Coop. Publ’g Ass’n v. Bresler, 398 U.S. 6 (1970)

Key point

There is no broad rule that calling someone a liar is never defamatory. Under Milkovich v. Lorain Journal Co., 497 U.S. 1 (1990), the question is whether the words, in context, convey a provably false factual assertion.

Practical answer

If you want a case for the proposition that calling someone a liar is not defamatory, you usually need a context-specific holding, not a categorical one. The strongest formulation from the Supreme Court is:

• Not actionable when used as rhetorical hyperbole or loose opinion: Greenbelt Coop. Publ’g Ass’n v. Bresler, 398 U.S. 6 (1970); Hustler Magazine, Inc. v. Falwell, 485 U.S. 46 (1988)
• Potentially actionable when it implies a provably false factual accusation: Milkovich v. Lorain Journal Co., 497 U.S. 1 (1990)

If you want, I can also find lower-court cases specifically holding that calling someone a “liar” was not defamatory under a particular state’s law.