For a djembe, I like tight rings. Ideally, once you have the loops on the crown ring, you should be able to push the crown ring down over the bearing edge (without skin) with moderate pressure, maybe assisted by a few moderate taps with a mallet. In practice, that works out to around a 4mm (1/6") gap between the side wall and the inside of the ring.
If the ring gets down to a 3mm gap, the knots on the crown ring tend to dig into the wood and make grooves as the ring is pulled down. That's too tight; you risk tearing the skin where it gets squeezed between the knots and the shell.
Up to a 6mm (1/5") gap is fine. I don't like rings larger than this because that increases the likelihood of skin slip and also starts to look poor.
For cow skin, add 1-2mm to the gap, to accommodate the thicker skin.
If you have rings that are on the large side, use thicker (5mm or 5.5mm) rope for the loops; for tight rings, go with thinner rope (3.5mm or 4mm). Don't go below 3.5mm because that tends to put too much wear on the verticals.
With thin rope for the crown ring, consider using double-strand loops as shown in the second image in
this post. This will be stronger and reduce the wear on both the rope for the crown ring and on the verticals as you tune the drum.
Cheers,
Michi.