Facebook – Limit of friend requests by day in Facebook

No, there is not a way to do that and I would imagine it violates Facebook policy

There's only the limit of having 5,000 friends and the unknown limit of friend requests you can send. The former is there because nobody can have so many active connections (if you're a public person wanting to be in touch with your fan base, you should use a Page not a profile). The latter is there to prevent spam and it's unknown for that reason.