tenderness has 11 distinct synonyms spread across 4 of its 5 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.
a tendency to express warm and affectionate feeling
a positive feeling of liking
“he had trouble expressing the affection he felt”
a feeling of concern for the welfare of someone (especially someone defenseless)
Synonyms, antonyms and the broader and narrower relations for tenderness come from Princeton University’s WordNet. Full sources and licences.