A relatively strong acid that does not employ borane, cyano, or halogen functions, containing only carbon, hydrogen and oxygen, is croconic acid. The structure of this acid from Wikipedia is given below:
(From WP user rohnjones) Wikimedia link
Croconic acid has two stages of dissociation, given in Wikipedia as $\pu{pK_{a1}}=0.80, \pu{pK_{a2}}=2.24$. The second stage dissociation especially stands out, being about two $\pu{pK_a}$ units or more stronger than most polycarboxylic acids (e.g., oxalic, malonic, tartaric, citric) and also stronger (in both stages) than other "ring" acids such as deltic or squaric.
The relatively strong diprotic acid character of this compound comes from the di-anion having aromatic character (mentioned in the Wikipedia article) plus the ability of a five-membered conjugate ring to take up negative charge, which is also compatible with aromatic coupling. The latter leaves less excess negative charge on the oxygens than is typical in acids containing carbon, hydrogen and oxygen only.