Best time for an "office hour"?

Perhaps it can be combination of 2 days with 12 hours difference in time.
Lets say (depends on most staff timezone)
1st - UTC Saturday 9AM (start of weekend shouldn't be a big deal)
2nd - UTC Sunday 9PM (end of weekend same as start)

Or in 1 day 2 times which requires more personal time from staff's.

(Hours are based on UTC by default, but it can be other zone which is common to staffs)

Without having a suggestion of my own, I'm inclined to disagree ...

Most people I know sleep until late on Saturday, and go rather early to bed prior to the first work day.

When we are targeting work days Monday-Friday many people can't give from their time to chat with CI staff, asking questions and etc. 
That is the reason for me to target Saturday/Sunday. I know that its personal time then but 1/2 hours isn't big deal.
For the time 9/21 UTC I have just mark it but its good to consider it with all staff's locations.
I think that is better to have it 2 times so all people even staff to have 1 chance to miss it and 1 chance to be in it..
As ciadmin mention at 2AM in his location he can be in a sleep but if there is second hour in 2PM he will be on without any problem

I don't disagree on the weekend, nor that an hour or two are an issue.

I disagree with the specific hours that you're proposing because the better half of Europe is in bed then.