I can't really tell you how to draw your graphs, because there are many different drawing and labeling conventions. A minimalist graph looks quite different from a classical transformationalist graph, and neither will look at all like a dependency or a traditionalist Reed-Kellogg graph.
What I can do is point out the major components of the sentence, which you can adapt to your specific needs.
The basic Subject/Predicate structure of your sentence is not ambiguous: the Subject is realized by the determinate noun phrase The poor child's story and the Predicate is realized by the verb phrase is sad. The VP consists of a copula realized as the verb is and its complement realized as the adjective sad.
The ambiguities arise in your parse of the Subject:
What's the function of the possessive? Is it a determinative, as in John's hat, or a modifier, as in men's clothing? That is, is this story one about or told by a particular child, or a story intended for children-in-general?
What does poor modify? Is this a story about or told by a particular poor child, or one intended for poor children; or is it a badly told story for children-in-general, contrasted with one or more well-told stories?
By the same token, which noun phrase does The determine -- the one headed by child, or the one headed by story?
Each of these choices will give you a different structure for the noun phrase, which you can represent according to whatever conventions you are called upon to use.