Anytime's rhymes with:
centimes, daytimes, halftimes, lifetime's, lifetimes, maritimes, nighttimes, oftentimes, pastimes, showtime's, wartimes
Anytime's sounds like:
amending, ammunitions, amounting, anding, animations, annotating, annotations, antenna's, antennas, antenucci, anthems, anthony's, antitank, antonacci, antonini's, antonio's, antonios, antoniu's, antonius, antonucci, antunes, antunez, anything, anything's