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.