Iny rhymes with:
binney, binnie, briney, finney, finnie, ginnie, ginny, glynnie, guinea, guiney, hiney, hinny, kinney, kinnie, kinny, linney, mackinney, mckinney, mckinnie, mckinny, mcwhinney, mini, minney, minnie, minny, ninny, phinney, pinney, pliny, quinney, skinny, sliney, spinney, swinney, tinney, tinny, vinnie, vinny, whinney, winney, winnie, winny, zinni
Iny sounds like:
i'm, iain, ian, ianni, iannone, ihnen, im, imai, imam, iman, imm, immu, immune, immuno, imo, in, in., ina, inane, inhuman, inhumane, inman, inmon, inn, inno, inoue, inouye, ion, iona, ione, iowan, iwan, iwen