From the episode:

O'Brien: "Well, we know one thing. They arrived before the year 2048."
Odo: "How can you be sure?"
O'Brien: "'Cause we were just there... And it's nothing like the mid-21st century I read about in school. It's been changed.. I mean, Earth history has been through its rough patches, but never that rough."
Kira: "If we limit our search to dates before 2048, how many possibilities does that leave us with?"
(Odo hands PADD to O'Brien)
O'Brien: "According to my calculations, three. But we only have enough chroniton particles for one more try."
Kira: "Well.. Pick one, chief! Lets hope you get lucky."
O'Brien: (examines the PADD for a moment, taps a date, hands it back to Odo) "It's by best guess."
Kira: "That's good enough for me."

We have a Bajoran, and alien shapeshifter, and Miles O'Brien on-hand. Kira and Odo have little to no knowledge of Earth's history (at least, pre-Federation (which was 2161, over a hundred years after 2048)). And just look at O'Brien's face when he's trying to figure it out:

Kira put him on the spot (not too unreasonable given the circumstances), and he made his best guess given the available information, since no one else was on-hand to help, and Kira, Odo, and everyone else was relying on him. His "best guess" is an estimated guess, given limited information.

The other two points in time apparently weren't critical moments, which is why he chose the Bell riots.

From the episode:

O'Brien: "Well, we know one thing. They arrived before the year 2048."
Odo: "How can you be sure?"
O'Brien: "'Cause we were just there... And it's nothing like the mid-21st century I read about in school. It's been changed.. I mean, Earth history has been through its rough patches, but never that rough."
Kira: "If we limit our search to dates before 2048, how many possibilities does that leave us with?"
(Odo hands PADD to O'Brien)
O'Brien: "According to my calculations, three. But we only have enough chroniton particles for one more try."
Kira: "Well.. Pick one, chief! Lets hope you get lucky."
O'Brien: (examines the PADD for a moment, taps a date, hands it back to Odo) "It's my best guess."
Kira: "That's good enough for me."

We have a Bajoran, an alien shapeshifter, and Miles O'Brien on-hand. Kira and Odo have little to no knowledge of Earth's history (at least, pre-Federation (which was 2161, over a hundred years after 2048)). And just look at O'Brien's face when he's trying to figure it out:

Kira put him on the spot (not too unreasonable given the circumstances), and he made his best guess given the available information, since no one else was on-hand to help, and Kira, Odo, and everyone else was relying on him. His "best guess" is an estimated guess, given limited information.

The other two points in time apparently weren't critical moments, which is why he chose the Bell riots.