While I agree it's best to apply online, day and time may still matter, because you may get "pending" (neither approved nor denied) online, and then may want call "recon" (short for "reconsideration"). And if you want to call right away, you can only do that if the bank's recon line is open.

Some banks (for example BofA) only have recon lines open M-F certain hours.

So I'd say either reserach when that bank's recon line is open (in case you'll have to call it), or apply during bank business hours M-F (in case you'll want to call right after applying and getting a "pending").