Summon Good Monster adds a few young dragons at the highest levels, iirc. A ring of Natural Attunement (Drake) also adds some drakes to creatures that can be summoned, but is quite costly.
This might be what you want:
Trompe l’oeil creatures are life-sized portraits animated by powerful magic or occult phenomena. Able to move and talk, these constructs can also step out of their frames to become three-dimensional beings. Born from artistic masterpieces, trompe l’oeils can easily pass for their original models, though close examination reveals that they are not flesh and blood, but only layers of paint. Trompe l’oeils can be created to act as guardians and spies, or on occasion, a painting will animate spontaneously. Rarely, a portrait is so lifelike, a nascent spirit is able to inhabit it. Believing itself to be as good as or better than the original, such a trompe l’oeil seeks to eliminate and replace the painting’s subject.
He could create a construct version of any corporeal creature with an Intelligence score. Admittedly he does need an existing dragon to paint a (life-sized!) portrait of, unless you / your GM tweaks the rules to allow portraits of imaginary beings.
I only found 2,
Draconic Ally, specially summons something that looks and acts like a dragon but is still technically summoned. Summon Nature's ally VII can be used to summon a Roc. Not exactly a phoenix but it's close.
Spells like Planar Ally and Planar Binding, could potentially be used on the creatures you describe, providing that it comes from another plane. However, this isn't the same as just summoning a creature since you're physically bringing them from their home plane and pressing them into service.
Closest I can think of is a summoner with a dragon eidolon and the summon eidolon spell.