"When my sister was six years old, she was attacked, set upon, by three Muggle boys."
"It destroyed her, what they did: She was never right again."
--Aberforth Dumbledore (DH28)
When Ariana Dumbledore was six years old, three muggle boys saw her doing underage magic. They demanded she show them what she was doing, and when she couldn’t, they attacked her. The event traumatized her, and led to the unraveling of the Dumbledore family.
Given that Ariana was six, and she was born in either late 1884 or early 1885, that would place this attack either at the end of 1890 or the first half of 1891. Percival Dumbledore was sentenced to Azkaban "scarcely a year" (DH2) before September 1892 (when Albus started Hogwarts), so it's likely the attack happened in 1891.