Budgeteer rhymes with:
racketeer, summiteer, austere, charpentier, crochetiere, frontier, marketeer, mateer, mcteer, minteer, pamphleteer, pelletier, profiteer, racketeer, stear, steer, steere, summiteer, teer, volunteer
Budgeteer sounds like:
baptistery, bedstraw, budgetary