Pigeon droppings can be composted – though it is best to only compost it from healthy, captive birds (such as racing stock), as poop from wild birds may contain harmful diseases or pathogens.
Like chicken poo, pigeon droppings can be a useful fertiliser in the garden but it needs time to “cool down” first. (It’s highly alkaline to start with and can burn delicate roots and stems of plants.) It will work as a compost activator in your heap – helping things rot down in a nice, timely manner – and the resulting compost will be great for your garden.
As always, it’s best to keep your compost heap balanced, made up of a range of different things, rather than just one thing – it’ll produce better compost quicker and with less smell. Since chicken waste is nitrogen-heavy, it is best added alongside “browns“, like wood shavings/sawdust or straw — perfect if you already line the bottom of your dovecote/nesting boxes with that sort of thing. If it’s not already mixed in with bedding materials like that, add it to your compost heap in moderation (1 part poo to 4 or 5 parts other stuff) and mix it in well.
If you’ve added a lot of pigeon poop to your compost heap, be careful using the resulting compost on acid-loving plants – the compost can still be leaning towards alkalinity even after it is rotted down.