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.
    some one
      from one
        End Rhyme Set #1 of 562 (Add to/Edit Set Members)
        other one
          another one
            End Rhyme Set #2 of 562 (Add to/Edit Set Members)
            twenty one
              any one
                many one
                  End Rhyme Set #3 of 562 (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
                      many one
                        Near Rhyme Set #1 of 79 (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 79 (Add to/Edit Set Members)
                                                                          Ericksen
                                                                            Erickson
                                                                              Ericson
                                                                                Ericsson
                                                                                  Erikson
                                                                                    Eriksson
                                                                                      Near Rhyme Set #3 of 79 (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)