WikiRhymer has about 9,000 rhyming words and phrases for "happy" starting with...

chappie
    crappie
      scrappy
        snappy
          papi
            crappy
              nappy
                unhappy
                  Cappy
                    • make it snappy
                    Pure Rhyme Set #1 of 1 (Add to/Edit Set Members)
                    Words that have a pure rhyme on their last syllable only.
                    therapy
                      chemotherapy
                        hydrotherapy
                          psychotherapy
                            immunotherapy
                              End Rhyme Set #1 of 995 (Add to/Edit Set Members)
                              campi
                                campy
                                  End Rhyme Set #2 of 995 (Add to/Edit Set Members)
                                  Shapley
                                    Tapley
                                      End Rhyme Set #3 of 995 (Add to/Edit Set Members)

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                                      Words that "almost" rhyme on the vowel-based rhyme sound of the stressed syllable like: be/eat or maybe/shapely. (Click for more info)
                                      campi
                                        campy
                                          Near Rhyme Set #1 of 126 (Add to/Edit Set Members)
                                          Shapley
                                            Tapley
                                              Near Rhyme Set #2 of 126 (Add to/Edit Set Members)
                                              raspy
                                                Gaspe
                                                  Near Rhyme Set #3 of 126 (Add to/Edit Set Members)

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                                                  Rhymes made up of more than one word. For instance, "jealous" and "tell us" or "shaky" and "make me."

                                                  We have no mosaic rhymes for "happy".

                                                  Mosaic Rhyme Set #1 of 1 (Add to/Edit Set Members)