Nothing in AltF Lexicon rhymes with antares. Its pronunciation ends in the phonemes TEHRIYZ, and no other entry in the corpus shares that ending. A word with a rhyme key of its own and no company is genuinely unrhymable in ordinary English — orange is the famous case, and this is another.
Two words rhyme when their pronunciations agree on every phoneme from the last stressed vowel to the end of the word. Nothing about spelling is consulted — that is why eight rhymes with freight and straight, and why cough rhymes with none of though, through or bough. For antares the matched ending is TEHRIYZ. The key is the pronunciation from the last stressed vowel onward, written in the CMU Pronouncing Dictionary's phoneme alphabet. Every entry sharing it rhymes.
antares has no rhyme. Its ending TEHRIYZ is unique among the entries in AltF Lexicon — no other word in the corpus is pronounced that way from its last stressed vowel onward.
Pronunciations and rhyme keys come from the CMU Pronouncing Dictionary; definitions and commonness come from WordNet and a corpus of everyday English. Full sources and licences.