You could use dry-wall adhesive or coving adhesive, as the surface you are bonding to is painted. It would be worth scratching the paint surface to create a key for the adhesive to take to.
When fitting the coving, if you panel pin the the lower edge of coving, it will help support it, whilst drying.
i use knauf cove addy i find it offers the longest working life so you can happily cut and fit a fair few bits without haveing to stop and knock up more gear
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