counter has 16 distinct synonyms spread across 7 of its 13 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
table consisting of a horizontal surface over which business is transacted
game equipment (as a piece of wood, plastic, or ivory) used for keeping a count or reserving a space in various card or board games
a calculator that keeps a record of the number of times something happens
(computer science) a register whose contents go through a regular series of states (usually states indicating consecutive integers)
a piece of leather forming the back of a shoe or boot
“a counter may be used to stiffen the material around the heel and to give support to the foot”
speak in response
“He countered with some very persuasive arguments”
indicating opposition or resistance
1 of the 13 recorded senses carries no synonym, antonym or related term, so it is not shown above. Every sense, with its definition and examples, is on the full entry for counter.
Synonyms, antonyms and the broader and narrower relations for counter come from Princeton University’s WordNet. Full sources and licences.