Answer: Unfortunately, shallow planters absolutely require more frequent watering than larger planters would. Any plant will need watering often, even if it is fairly tolerant of dry soil. You could try using a water-holding polymer mixed into the potting mix (some formulations include it already) and see if that helps. Read and follow the directions for how to use it. But daily watering in the summer, possibly even twice a day, would not be unusual if the containers are relatively small and the plants have grown large.
Petunias are relatively drought resistant and do well in hot full sun, but you might also try Callibrachoa (million bells), dwarf cosmos, dwarf marigolds, Portulaca, and possibly some mixed succulents (from the perennial section of the nursery, they have interesting foliage but are not colorful with flowers. Although perennial, I would not expect them to be reliably hardy in a container.) Your local professional nursery staff may have some additional suggestions.
As far as pigeoons go, I do not know of any plants that would deter them. Some people report success using fishing line strung just above the plant tops to confuse birds and prevent them from landing, perhaps that would help with pigeons, too.
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