This method wraps Sunbrella cloth around the old grommets so you don't have to do any grommeting. This catamaran is a Hobie 16.
I used a similar method to re-tramp my Hobie 18 with PVC/Polyester truck tarp.
If your tramp is totally gone, there's an easy method for that too.
Catamarans you get for cheap or free will need a new trampoline.
Trampolines get destroyed by UV from sitting out in the sun.
In case you're looking for a way to fix the kind of trampoline you bounce on, this same method would probably work fine for that.

I used Sunbrella UV-resistant cloth for the new tramp so it will last longer than the original one.
For comparison, here's how I re-tramped my Hobie 18 with PVC/Polyester truck tarp material.

Here's Damon, Audrey, and Star on the test voyage. The new trampoline works great!
The other photos below are top views of the boat before and after re-tramping.

Step 1: Take Pictures of Your Old Tramp

Take lots of pictures of how it was. You'll need them later when you're wondering how to put it all back on.
The frame of the catamaran is made from sections of aluminum mast extrusion. There's a slot in the edge of the extrusion. The sections of trampoline cloth have a piece of polypropylene rope sewed into the hem. That rope hem gets slid into the slot. That's how the cloth gets attached to the frame.

If your boat has no tramp at all and you're starting from scratch, don't worry.
These photos will give you an idea how the tramp used to be.
The grommets on the tramp are really massive. If you're making a tramp from scratch and don't want to mess with grommets, just sew a rope into all the edges of the cloth and lace around that.

Step 2: Unlace and Remove the Two Big Sections

Unlace the ropes from the tramp.
Along the back edge of the frame is a narrow strip that's just wide enough for a row of grommets. Leave that where it is, it's fine.
Slide the two big pieces out of the frame. Try to keep them in one piece if you can. The cloth will look terrible, but only the top surface is shot. The edges have multiple layers so they'll be fine.

Then cut the stitching holding the footstraps. Do it carefully so you can re-use them.
If they're gone or too weak, get a piece of seatbelt to replace them with.

Step 3: Sew It to an Oversized Piece of Cloth

I scavenged some scraps of "Sunbrella" UV resistant cloth from a sailmaker's dumpster.
Boatyards and awning shops are other good dumpsters to watch.
I sewed some scraps together to make a big piece a few inches bigger than the halftramp on all sides. I used the "flat felled seam" which is the strong seam used to sew jeans.
If you start out with a big enough piece of cloth you won't have to mess with that.
Look for something synthetic and UV resistant that's as strong as canvas. If it's a porous mesh, that's even better, the wind won't have as much to push on when it's flipping you over.

Lay out the new piece of cloth on the ground.
Flip the old halftramp over and lay it on the new cloth.
That old tramp has already stretched and the new tramp is going to stretch.
So push the edges in so the new tramp will be smaller Trace around the edges of the old tramp so you'll know where they go.

I'm using a really nice industrial machine with a fat needle. So I'm sewing through the thick cloth.
If your machine is wimpy, you don't have to do that. In that case fold the new cloth around the old edge and sew your cloth to itself.

Step 4: Cut Off the Rotten Flesh

Now that the skin graft is in place and the wound is stabilized, cut off the old rotten part in the middle.
Notice how I've cut the corners off the new cloth also.

Step 5: Cutting Corners

Cut the corners of the new cloth as shown.
You're going to have to shove the rope edge into the slot in the aluminum frame, so don't end up with too many layers of cloth anywhere.
I used "pinking shears" to make a zigzag edge that unravels less. You could also melt the edge.

On second thought, don't worry about any of that, this is supposed to be a quick job, and the boat won't be worth real money regardless of what you do. It's only worth sailing, so hurry up and get to that.

Fold the edges of new cloth over the top of the old edges and sew them down. Don't sew into the old grommets, that will break a needle.

Sew the the foot strap to the trampoline.

Step 6: Install Your New Tramp

Rush out to the boat with your first finished tramp half.
Make sure you can slide it into the frame.
Then go finish the second half of the tramp and slide it into place also.

Stab slits through the grommet holes as shown

Step 7: Lacing

Shove a skinny needle nose plier through the grommet. A hemostat also works well.
Grasp the end of the lacing rope and pull it through the grommet.

Step 8: The Underside

Here's what the tramp looks like from underneath.
Notice the reinforcing patches for the foot strap.
The flaps of folded-over cloth around the edges are all different widths.
It will probably last longest where it's thickest.

Step 9: Lace the Corset

Lace the trampoline tight.
Be amazed how much it stretches.
Be glad you made it smaller than the old one.

Go sailing!

If your cloth isn't UV resistant, make a cover out of silvertarp to protect your tramp when it's parked outside.