You can of course use a non-standard contract. It's called a pre-nup, and it has both the downsides and upsides of a non-standard contract.
I don't have, want, or even particularly like children, and even I have a problem thinking of them as "shares" or "assets" or pre-deciding their fate with a formal contract written before they were born or old enough to express their own wishes.
I'm sure if you were the dictator and God-King of a small country, where you could reinvent society as you wish, you might be able to create something that would fit 99% of the population, since you would be able to forcibly squeeze the behavior of each couple into a few standardized containers with corresponding legal rulesets.
Getting married is romantic and irrational, and that's why we enjoy doing it.