The early morning time periods would be best because fewer people in general will be donating to other charities.
More than one 2-hour time period can be targeted if everyone makes a donation during each time period. Just make the donations smaller. For instance, make a $5 donation at 1 AM and another at 3 AM instead of a single $10 donation at 1 AM. Or three time periods can be covered by making $3 donations at 1, 3, and 5 AM. Of course, getting up 3 times in the middle of the night would be a pain.