Peaches are a soft, juicy summer fruit that birds can enjoy — with the same important rule that applies to all stone fruits: the flesh is safe, but the pit is not.
The short answer
Yes — birds can eat peach flesh, but never the pit. The sweet, soft flesh makes a lovely treat, but the stone (pit) contains compounds that release cyanide, so it must always be removed and kept away from your bird.
Why the pit is dangerous
Like cherry, plum and apricot stones, a peach pit contains amygdalin, which releases cyanide when crushed. For a small bird this is a real hazard, so never let your bird near the stone.
How to feed peaches
Wash the peach, remove the pit completely, and offer a small piece of ripe flesh. The washed skin is fine to leave on. Keep it a treat, as peaches are sugary, and offer a small amount occasionally.