It's difficult to give a single answer as to when these times would be, but if your target audience is school students then they are more likely to be online just after school (~4pm - depending on exactly when they finish school) and at weekends, whereas if you are targeting working adults then lunchtimes and later evenings might be the best time.
If possible you should do some research to find out when your users are online and likely to see the content. If you can access logs of when users have visited the site so that's a good starting point, however, with a public platform like Facebook that won't always be possible.
After that you want to make sure that the content is going to be visible for long enough for most of your target audience to see it. On a busy site you might not have very long before other posts push yours down the page, so you need to pick your time with care. If it's really important you could consider pinning the post in some way so that it stays visible for longer.
Some sites (like Stack Exchange and Facebook) will republish a post to the home page if it changes in some way (edits, replies, comments etc.) so you could periodically prod the post in some way so that it reappears on the home page. Be careful with this though, some sites (especially Stack Exchange) take a dim view of someone making meaningless edits to their posts just to bump them.
The other thing to consider is sharing links to your post on other social media platforms at different times of the day to catch a wider spectrum of your audience.