You best course is to sweeten the wine to your taste preference. Tartness of the wine is from its acidity and the right balance of sweet&sour is personal.
The other way to achieve balance is by lowering the acidity through addition of potassium bicarbonate or similar agent. In your case, I do not recommend this course since you do not have a pH meter and won't be able to tell if you drive the pH too high, which increases the risk of spoilage/oxidation.
Cooling plum wine may not result in potassium bitartrate precipitation (aka wine diamonds). You need a sufficient concentration of tartaric acid in the wine for this to occur. While grapes are loaded with tartaric, the primary acid in plums is malic which will not form insoluble salts and precipitate. Of course if you added an acid blend in your recipe, that will change the acid mix.