Nettle is a good dye, but it needs a mordant to help fix it.....the site referred to suggests vinegar, however, experience shows that vinegar won't work, you'll get a pale stain not a good dye using it.
Sisal is a woody fibre and as such it really needs to be tannined to take a dye; however you could try copper and then boil up the nettle with some really strong tea too, that ought to give you a brownish green.
Copper mordant is
toxic
but if you use it carefully then it's awfully useful. Find some off cuts of copper plumbing pipe, or something similar, and put them into a disposable screw top jar. If you use ammonia to cover the copper pieces you will very quickly get a bright ink blue liquid. If you use vinegar you will get a pale turquoise coloured one instead. Leave overnight. This liquid is the copper mordant.
Put hot water into a bucket and strain in the mordant liquid. You need enough water to just cover your net and allow you to move it around. Put the net into the bucket, stir occasionally and leave for at least a good couple of hours.
This mordanting leaves the surface of the sisal receptive to the dye. Boil up *lots* of nettle leaves and tops, strain and add to the contents of a really strong pot of tea.
Meanwhile, since you don't want the dye to fix to the loose copper in the mordant liquid you have to strain out the net and rinse gently. Remember the copper liquid is toxic and has to be disposed of safely. The sewerage systems are used to a little copper, since it's used in central heating and domestic potable water supplies, but in concentration it kills plants and animals.
Put the net back into the bucket and pour the dye you've made over it. Make sure there's enough liquid, even if you have to dilute it down a bit, to cover the net and let you move it around.
If you can do the dyeing using heat it will work very much more quickly, but time works just as well. Haul out he net, rinse and hang to dry. It ought to be a muted bushcraft green
Best of luck; let us see some photos?
Cheers,
Toddy