It's best to make two separate cough syrups, really.
That's because the tasty syrup will be gone by the time you get a cough, while the less than tasty one will keep.
So here's the tasty herb mix for making a cough syrup:
2 parts peppermint (Mentha x piperita)
1 part hyssop (Hyssopus officinalis)
½ part thyme (Thymus vulgaris)
And here's the less than tasty herb mix for making a cough syrup:
2 parts peppermint
1 part hyssop
½ part thyme
½ part horehound (Marrubium vulgare)
40 g fresh chopped herb (or far less dried herb)
9 dl water
450 g sugar
Put herb + water into a pan, bring to a boil. Cover, turn heat down, let simmer for 20 minutes.
Let cool, strain liquid into a measuring jar while pressing all the goodness out of the herb. Clean your pan and pour the liquid back. Put the pan back on the stove, without a lid, and let the liquid evaporate slowly on low low heat.
Add the sugar when you have only 2 dl liquid left. Stir until the sugar has dissolved. The syrup can simmer but it shouldn't boil.
Pour your syrup into a glass jar with a tight-fitting lid, and keep the closed jar in the fridge.
If you did things right your syrup won't crystallize (too much sugar - that is, you evaporated off too much water) during the first few months, nor will it ferment (too much water).
It's best to use a small pan for this, as it's easy to evaporate off too much liquid in a large pan while you wait for the sugar to dissolve.
Also, don't let things evaporate until you have less than 2 dl left. A syrup made with 1 dl simmered-down liquid that's then brought back to 2 dl by adding water tastes like it should: ghastly. Check every half hour until you have 3 (or so) dl left, then check every 10 minutes.
That peppermint-hyssop-thyme syrup really is tasty. Mmmm.