They talk about:
- The type of people that come to the park
- The type of food they leave
- Relations with other female pigeons or 'birds'
- Funny scenarios where they've poo'd on people
These common topics then lead to deeper and more thought provoking topics like whether the egg came before the chicken and so on. The humor will be that both pigeons are talking in such a colloquial human way but what they are talking about is something no human can discuss in that perspective.
I will start working on the order of the topics and how the dialogue will get from talking about one subject to another