In each case, the second is more natural, first is old-fashioned. Use the second

I can eat no more. <-- used for emphasis I can't eat any more. <-- more common. It should be "any more" because you're talking about a quantity. I can have kids no more. <- awkward. Instead say "I can no longer have kids." I can't have kids anymore. <-- In both sentences, you should really say "children" because the subject is serious. I could work there no more. <-- It would be better to say "I can no longer work there." I couldn't work there anymore. <-- correct I want no more excuses. <-- correct. Again, this is used for emphasis. I don't want any more excuses. <-- correct Note: "anymore" means "no longer". "any more" is used when discussing quantity (like food in the first examples, or when comparing things, "I don't like her any more than I like him."