I can't imagine that a seller would reject an otherwise solid offer because the deposit wasn't what he wanted.If the house works for you, I'd write the offer and let them accept, reject or counter. 

We threw out a number today to try and start negotiations and got rejected without counter.

I’ve had offers rejected without a counter and offers ignored.

Is it enough to just reject them based on "not meeting the credit criteria" or do they need something more specific?

I have an offer in on a house in Baltimore right now, but I don't know if it will be accepted or rejected.

He doesnt meet income and she doesnt meet credit is a no go for me as an unmarried couple Yes that was my thoughts exactly, I called and let him know we would not be proceeding with the application and he was super polite which made the rejection harder.

Why are you rejecting applicants?

I'm entering month #2 in my 3rd door search and was getting dissapointed, all my offers getting rejected. 

The seller can reject your contingencies but there's no risk to you if you structure your offer properly. 

In my way of thinking i'd rather make 10 low offers and be rejected on 9 so I can get the one that accepts at a good price.