Sindarin for "Tale of the Children of His Lies"

Would this be correct?

Narn-i-Chîn Cauthdied

Narn-i-Chîn is Tale of the Children.
Cauth is a deception/lie. Died is a suffix meaning his.

I believe it would be Narn Hîn i·Choeth dín. Tale (of the) Children (of) his Lies

cauth is singular you need the plural coeth.

Tolkien gave Narn-i-Chîn Hurin as the Tale of the Children of Hurin

Yes, he did but that does not include a possessive, so that changes things a little bit from my understanding.

I read the rules on this stuff. I really do. But I usually don't understand them. They might as well be written in Greek or Basque.

Thanks ever so much for your help.

This is a note from Ellanto on VL:

What I refer to as a "genitive construct" is the kind of genitive formation characteristic of Semitic (or perhaps Afro-Asiatic) languages on the one hand, and Insular-Celtic languages on the other hand; I am not aware of any languages outside these two families that have this type of construction, but please correct me if I'm wrong. What sets these genitive constructs apart from other types of genitive formations is that only the final noun in the sequence of nouns in a genitive relation can take on the definite article, and if the final noun is definite, then the entire phrase is treated as definite for all intents and purposes. In other words, we have the following pattern in Celtic and Semitic languages:

• X Y the-Z = "the X of the Y of the Z"
• X Y Z = "an X of a Y of a Z"
• Putting an article in any other place is entirely ungrammatical. The evidence we have in Sindarin fits with this pattern, with the exception of 5 examples, which is why this pattern is relevant.

As far as I am aware, the majority of syntactical analyses of genitive constructs in Hebrew agree on the general principle of how these formations are derived in such a way that the definite article is blocked everywhere except on the last noun: movement of the head noun (the possessed item) from its base position upwards to where the definite article would be (the last element does not move, because it is not itself the head of a construct, and so it can have an article). I have seen some non-movement analyses, for both Semitic constructs and Welsh, but they are riddled with theoretical and empirical problems, often to the point of not providing any explanation for the lack of articles to begin with, and as such it seems reasonable to assume that the movement is necessary.