Would coconut milk be an ok alternative to the yogurt?

If you want to use something vegan to replace 2c yogurt, try something of same density like soft tofu or coconut yogurt.
If you use 2c of coconut milk, I think the result will be too loose. Maybe start with half cup coconut milk and add more to taste.

Not sure, but search the vegan version of this dish easily available online. It uses a cashew but paste and plant milk in place of the yoghurt. It’s equally delicious.