There are several synonyms for the phrase "bonds of amity" which means strong bonds of friendship. One of the synonyms is "ties of camaraderie" which implies a strong sense of loyalty and trust among people who share a common goal or interest. Another synonym is "connections of affection" which suggests an emotional connection between people who care for each other. "Alliance" is also a synonym and implies a mutual pact between parties with common interests. "Fellowship" is another synonym, which means a group of people who share a common interest or purpose. In summary, the phrase "bonds of amity" can be substituted with any of these synonyms based on the context of its use.