The phrase "cockles of one's heart" refers to a person's deep and genuine affection or love for something or someone. In terms of synonyms, one may use expressions like "core of my being", "heart and soul", or "deepest feelings". Other similar phrases include "my heart sings", "warms my heart", or "brings joy to my heart". These phrases allude to the intense emotions that a person feels towards something or someone, and are often used to express an individual's appreciation or gratitude towards whatever is causing them to feel such intense emotions.