Creakign from the stabiliser is almost 100% due to contaminated friction pads - the only other probable cause is cracked or broken pad (usually from dropping the tow-hitch onto the tow-ball)
Let's assume it a dirty tow-ball, so make sure all paint or plating has been removed from the tow-ball, that's it's clean and free from rust or other contaminants.
Then clean the friction pads inside the coupling head - you can do it in place - just use clean cotton rags and keep wiping until any deposit has dissappeared (white rag is best for this)
That should fix it - but if there is fgrease or oil contamination then either white spirit or brake cleaner will help it to be wiped off.
If it still creaks after all this, then a final things to check:
1. Remove the pads and see if they are cracked - replace and don't drop the coupling onto the tow-ball again
2. If the pads are in one piece, but obviously look engrained with contaminants - then resurface the pads with emery paper
3. If this fails then replace the pads
4. If this fails then replace the tow-ball - some tow-balls are mirror smooth and some have a very noticable set of machining groves running around the tow-ball - like our Bosal detachable - and those with goves seem to be the quietest - but getting a different tow-ball can be a lottery.
Robert