I have never heard of "counter purpose" as an expression, and "counter-porpuse" is definitely wrong. As the others said, you need "counter proposal" in this context.

Those two convey entirely different implications. Counter-proposal suits your sentence best. It means "return proposal made by one who has rejected a proposal." On a separate note, I suggest cross-purpose instead of counter-purpose. So as a suggestion: We were trying to get a 60% of the contract to carry out the project, but the investor rejected it days later. He offered me a 50% counter-proposal contract, which was agreeable for us, and we finally accepted it."

Nope, they do not mean the same thing. In the sentence that you gave it is best that you simply use counter-proposal. Let me know if you need anything else :)