Missionary rhymes with:
expeditionary, cautionary, concessionary, confectionary, confectionery, counterrevolutionary, deflationary, dictionary, discretionary, disinflationary, evolutionary, expansionary, expeditionary, functionary, inflationary, noninflationary, probationary, reactionary, recessionary, revolutionary, stationary, stationery
Missionary sounds like:
machamer, machinery, macmurray, macnair, macnamara, magaziner, magner, manganaro, masoner, masonry, mcenery, mcenroe, mchenry, mcinroy, mcmorrow, mcmurray, mcmurrey, mcmurry, mcnair, mcnairy, mcnamara, mcnamer, mcnary, mcnear, mcneary, mcneer, mcnemar, megner, meisenheimer, meisner, meissner, meixner, mesmer, mesner, messamore, messimer, messmer, messmore, messner, michener, miesner, misener, misenheimer, misner, misnomer, missimer, mixner, mizner, moessner, monsignor, muchmore