I have tried a couple of different apps for iPhone that would allow me to schedule messages to send at specific times, but have only found one that actually works as advertise. The Auto Sender is an app that will let you choose a time, select one or multiple contacts, and then the message will automatically send at that time.
This is much more convenient then apps that will only send you a notification letting you know that it is time to send the message. You can simply schedule the message, and not have to worry about it.This means the message will send, even if your phone is turned off! This app has worked great for me so far, I have been using it for the past few months and all my messages have been sent on time!