If your website's # of visitors produced a weekly bell curve, with say Sunday generally being the lowest and Wednesday or Thursday being the peak... What day of the week would be best to regularly add major content updates?
Though sunday seems the logical conclusion,do inform your users in advance that you will be bringing the site down on Sunday during this time period (mention the time zone too) so that people are aware of it well in advance and are not surprised to find it down.
When your site is down do provide an informative or even fun message which tells them when the site will be back up.
Assuming you don't require downtime...
If you want user feedback prior to the "busy hours" (so you can make amendments), perform update on lowest demand.
If the update doesn't require feedback and you want users to feel like they are getting the newest content, perform the update prior to the peek (e.g. at 50% of the expected peek on the way up to the peek) so that the peek users will get the freshest content.