I have found that the classic binder reinforcement rings are not the best choice for plastic parachutes.  A few times when I used a rather strong string for the shrouds, they are able to cut right through the plastic and the reinforcement ring. Another problem with the rings is the adhesive used, they seem to dry out after a while (years).

Instead, I found that a small square or strip of plastic/vinyl electrical tape is stronger than the binder reinforcements. Place a strip of electrical tape under the hole in the plastic parachute, between the hole and the edge of the parachute. Even if your parachute has reinforcement rings already, just add this on top of those.  You don't even need to surround the entire hole. This vinyl is much stronger and can be made larger, and the larger it is the more it spreads out the load on the plastic. Furthermore, the adhesive in electrical tape is designed to stay sticky for many decades - you don't want electrical tape to fall off inside an electrical box with 200 volts in it - do you?

Another tip that improves the strength of the connection is to fold the corner/tip of the parachute over a bit (on the inside) so that the shroud passes between two layers of plastic. Be sure to reinforce both pieces of plastic to get the most benifit.

If you are into appearances, you can usually find electrical or vinyl tape in an assortment of colors, so choose orange, red or whatever. It doesn't have to be regular old black.