Fix drywall that lost strength due to hanging curtain rod
As you have found out, curtain rod supports do not do well hanging from plaster anchors. They really should be attached to studs, but where that is impossible, toggle anchors give you a chance at success. I prefer the solid bar type that pivots after insertion.

The drywall in the immediate vicinity is beyond saving. Even toggles will not have much solid to support them. You need to move the bracket well away from the damaged area (to a stud if you can), or you need to build up the area to support it.

One way to reinforce the area is to create a wooden backing behind the drywall to serve as a support. Find a piece of wood at least 1 1/2 inches wider than the space between the screws. Cut it to about 6 inches in length.

Cut away the damaged section of drywall making a hole a bit wider than the board and about 3 inches high. You are going to insert the board vertically into this hole and attach it to the back of the drywall. 

An easy way to do this is to drill a small hole in the center of the board and tie a string through the hole. You can then insert the board and use the string to prevent it from falling and to manipulate it into place.

Screw through the drywall into the board using drywall screws. Use two screws top and two on the bottom. This locks your new framing piece in.

Make a patch of drywall and fill the hole. Tape and patch with joint compound. Lightly sand and prime. Paint now or later.

Now, when you reattach the bracket, you will be screwing into the wood which is supported by many square inches of drywall. I would predrill the holes with a bit slightly smaller than the screw body to reduce the chance of splitting the wooden backer.