Battleship rhymes with:
consulship, generalship, consulship, generalship, airship, ambassadorship, apprenticeship, authorship, bipartisanship, blankenship, brinkmanship, brinksmanship, censorship, chairmanship, championship, citizenship, companionship, conservatorship, consulship, craftsmanship, dealership, dictatorship, directorship, distributorship, draftsmanship, editorship, fellowship, flagship, gamesmanship, generalship, governorship, gunship, headship, homeownership, internship, judgeship, kinship, leadership, lightship, manship, membership, one-up-manship, one-upmanship, ownership, partisanship, partnership, premiership, professorship, proprietorship, readership, receivership, relationship, ridership, salesmanship, scholarship, showmanship, spaceship, speakership, sponsorship, sportsmanship, starship, statesmanship, steamship, stewardship, trusteeship, upmanship, viewership, warship, winship, workmanship