Don't know of any sites that will allow that. Do it via email. Make it clear to everyone involved what the expectations and rules are.
I did one once where we drafted one round per day. 12 people, so started at 8 am. Player 1 had from 8:00 to 8:59 to pick. Player 2 had anytime until 9:59 to pick. etc. We did it where if Player 1 picks at 8:05, Player 2 still has until 9:59 to pick. If he picks at 8:30, then great, but Player 3 still has until 10:59 to pick. That way every owner knows to block out some time during their hour to dedicate to the draft. Took us 15 days to do the draft, but it worked. Helps if you send a note each day reminding everyone what their hour is for that day, since in a snake draft it'll be different every other day. Use that daily email as a way to "clean up" the draft list, organize it into rounds, etc (Assuming you're the commish).
Or if you'd rather it keep going naturally, at least set rules such as 2 hr time limit between picks, clock starts once previous person replies-all with their pick. And have a reasonable cutoff time every night and a restart time every morning (i.e. Pick 3.03 made at 9:00 PM, nightly cutoff at 9:30 PM, draft restarts at 7:00 AM so next pick needs to be made by 8:30 AM).
Set whatever rules you want. If you're too lax though, then it becomes where one person holds up the draft, and it becomes the responsibility of the commissioner to have to chase them down and constantly babysit to make people hurry up if they're taking too long. Tell everyone to keep a list of who's already been drafted. If someone drafts a player that was already taken, then set a rule for what to do.
Email drafts can be fun, as long as there are rules in place.