My wife and I are traveling to New York soon. What are the best discounts for the new users?
IDK About Lyft, but for Uber, use a signup code to get a free ride:
http://forum.mrmoneymustache.com/welcome-to-the-forum/free-$30-uber-ride-%28uber-referral-thread%29/
Then once you have that account, use THAT account's sign up code to sign up the wife with that code. Then you'll earn 3 (the inital signup for account 1, the initial signup for account 2, and the referral from account 2). You can also post your referral code in that thread and maybe get another one from someone using it.
That's the basic way to get a few free rides without resorting to making up fake emails and using extra devices to earn more.
Also, i want to do all the signups for both apps before going to the trip so i want to make sure the credits are in my account beforehand. How long does it take for these discounts to expire after signing up? How many discounts can i get per app?
They last a few months. They used to be $30, but they're $25 now, IIRC. As many separate discounts as you want (one per account when you sign up, and then an account can earn multiple for referrals).