Amber-coloured gum coming from stone-fruit trees (plums, peach, etc) is usually a symptom of canker, which is a bacterial infection.
I believe that the remedy is surgery.
"Cankers often follow winter damage, sunscald or insect damage. After infection, the wounded tissue exudes large amounts of amber-colored gum. Later, the infected bark cracks open and the affected tissue turns black. Cankers should be removed by pruning; between cuts, disinfect pruning shears with an alcohol or bleach solution."
There's also something about treating canker on damson trees on this page (quite a way down the page):
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Amber-coloured gum coming from stone-fruit trees (plums, peach, etc) is usually a symptom of canker, which is a bacterial infection.
I believe that the remedy is surgery.
"Cankers often follow winter damage, sunscald or insect damage. After infection, the wounded tissue exudes large amounts of amber-colored gum. Later, the infected bark cracks open and the affected tissue turns black. Cankers should be removed by pruning; between cuts, disinfect pruning shears with an alcohol or bleach solution."
There's also something about treating canker on damson trees on this page (quite a way down the page):
http://www.bbc.co.uk/lancashire/content/articles/2008/01/08/damsons_feature.shtml
Have a look at my answer to this question here, too, for more treatment details.