I wouldn't give them too long, probably not over a couple of days. I haven't rented much, but it has happened that I gave someone information, even spent time checking with Member Services for availability in multiple combinations, and after letting them know, never heard any response from them at all. Some people just aren't as polite as you would wish.
And, unfortunately, some people want it for free, or are just jerking you around.
Maybe it would help to say "Here is your info, if I don't hear from you in x amount of time, I'll assume you are not interested."