In 1978 only half the women granted child support by a court received

Unfortunately the issue with (C) is largely idiomatic. Consider some simple examples:

"Tim had any money in the piggy bank." - Not okay
"Tim had some money in the piggy bank." - Okay
"Tim had no money in the piggy bank." - Okay
"Tim did not have any money in the piggy bank." - Okay

Here are some similar examples that look a bit more like what we have in this question:

"The women had any support agreements." - Not okay... and (C) has the same incorrect structure (the only difference is the "not", which makes the verb negative).
"The women had some support agreements." - Okay
"The women had no support agreements." - Okay... and this is pretty much what we get in (D).
"The women did not have any support agreements." - Okay

Another problem with the "had not" in (C) is that it causes the reader to anticipate a past perfect verb. For example:

"Tim had not finished getting dressed when his Zoom meeting began."

"Had not" anticipates a participle ("finished") to complete the past perfect verb ("had finished").

So, the "had not any" in (C) is not idiomatic and, more importantly, it's confusing. That makes (D) a better choice.

Also, keep in mind that this question is OLD. Probably older than most people reading this thread. So don't lose too much sleep over it.

I hope that helps a bit!