Hello there,
I could build a dating site with registration, login, profile editing, photo upload and a chat system for 250 USD to fit your budget limit in 10 days.
I am working with bootstrap so I'll make it responsive, I can add a minimal administration back end to allow you to manage users.
Although I'd need more details about how complex would you want it or maybe some examples.
So far I can promise you a very simple yet fast dating website.
Regards,
Calin.