At various points, the HRE served as close to a puppet of the English or Dutch (cash for loyalty, basically). Of course the internal politics were mostly beyond their influence, and the HRE danced happily between near-puppet and ally.
Rome at some points had several of the Macedonian successor states as basically puppets (prior to annexation), which were pretty big if fragile powers.
British India, crazy conglomerate between Company and puppets as it was, operated close to as a big puppet (i.e. the government was independent from the British one, even if strongly influenced, and its having nominal independence is dubious). Same-ish for the DEI.
Late in WW1, Austria-Hungary was devolving into a German puppet (from its earlier status as a seriously inferior ally).
And of course, for bits of the 19th century, the Ottomans were close to a British-French protectorate (if not quite puppet).
Rome at some points had several of the Macedonian successor states as basically puppets (prior to annexation), which were pretty big if fragile powers.
British India, crazy conglomerate between Company and puppets as it was, operated close to as a big puppet (i.e. the government was independent from the British one, even if strongly influenced, and its having nominal independence is dubious). Same-ish for the DEI.
Late in WW1, Austria-Hungary was devolving into a German puppet (from its earlier status as a seriously inferior ally).
And of course, for bits of the 19th century, the Ottomans were close to a British-French protectorate (if not quite puppet).