How long does it take for a suppository to relieve constipation?

Usually < 1 hour. I depends on the suppository. Some are glycerin and only stimulate the rectum by their irritant properties. Bisacodyl suppositories ( dulcolax, etc.) are gut stimulants and generally work better and quicker but can lead to cramps.
Quick. Most suppositories if used as instructed will take effect within 4-6 hours.