WikiRhymer has about 6,000 rhyming words and phrases for "heroin" starting with...

heroine
    Pure Rhyme Set #1 of 1 (Add to/Edit Set Members)
    Words that have a pure rhyme on their last syllable only.
    other one
      another one
        End Rhyme Set #1 of 552 (Add to/Edit Set Members)
        twenty one
          any one
            End Rhyme Set #2 of 552 (Add to/Edit Set Members)
            wore one
              poor one
                End Rhyme Set #3 of 552 (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)
                twenty one
                  any one
                    Near Rhyme Set #1 of 78 (Add to/Edit Set Members)
                    baron
                      barren
                        heron
                          marron
                            perron
                              lebaron
                                Aaron
                                  Aran
                                    Aron
                                      Barron
                                        Charon
                                          Charron
                                            Farren
                                              Farron
                                                Ferren
                                                  Ferron
                                                    Herren
                                                      Herron
                                                        Karen
                                                          Karon
                                                            McFerren
                                                              Sharon
                                                                Theron
                                                                  Veron
                                                                    Yaron
                                                                      Near Rhyme Set #2 of 78 (Add to/Edit Set Members)
                                                                      Ericksen
                                                                        Erickson
                                                                          Ericson
                                                                            Ericsson
                                                                              Erikson
                                                                                Eriksson
                                                                                  Near Rhyme Set #3 of 78 (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."
                                                                                  • arrow + one
                                                                                  • narrow + one
                                                                                  • narrow + run
                                                                                  Mosaic Rhyme Set #1 of 1 (Add to/Edit Set Members)