(Source: Pierre Duhem, 1908, To Save The Phenomena)
According to Duhem, Ptolemy’s model was the first to fit observation - i.e., to “save the phenomena” of planetary motion. What Ptolemy did that previous philosophers had failed to do was to combine epicycles and eccentrics - each planet being borne of an epicycle whose centre described a circle eccentric to the world.
The reason that Ptolemy was the first to combine the two appears to be that Hipparchus proved that his model could be formulated using either epicycles or eccentrics.
What Hipparchus proved was that the course of the sun can be represented either by supposing that this star describes a circle eccentric to the world, or by letting it be carried by an epicycle, provided the revolution of this epicycle is achieved in exactly the same time in which its centre has completed a circle concentric with the world.
Having demonstrated the equivalence of the eccentric and epicyclic hypotheses, subsequent philosophers used either one or the other, but not both, thus failing to save the phenomena. Only Ptolemy combined the two to save the phenomena.
Although Hipparchus did not extend his model to include the planets, Theon of Smyrna, in his Astronomia, wrote that Adrastus of Aphrodisias said Hipparchus held that his method could be applied to each planet.
So who tried using epicycles between Hipparchus and Ptolemy?
By the time of Hipparchus astronomy had come to be dominated by the peripatetics - i.e., the followers of Aristotle’s physics - and they weren’t having any of this epicycle nonsense. For the Peripatetics, epicycles/eccentrics were contrary to natural principles.
Prior to Aristotle, Plato had declared astronomy to be the domain of the mathematician and had appealed to mathematicians to formulate a purely mathematical astronomy which “saved the phenomena” of planetary motion. Plato’s attitude was that the human mind was too feeble to comprehend the true nature of the superlunary spheres and therefore we must be content to have a mathematical theory which at least allowed us to make predictions that fit observation regardless of “truth”.
According to Duhem, almost all of what we know of the period between Hipparchus and Ptolemy consists of the peripatetic criticisms of epicycles/eccentrics. However, Duhem does cite the example of Adrastus of Aphrodisias who lived shortly before Ptolemy and proposed a model using epicycles.
According to the testimony of Theon of Smyrna, Adrastus of Aphrodisias ascribed to each planet an orbital shell contained by two spherical surfaces concentric with the universe. Within the shell is a full sphere occupying its entire thickness. The planet is then set into this full sphere. The orbital shell carries the full sphere in its revolution around the centre of the world while the full sphere turns on its axis. By means of this mechanism the planet describes an epicycle whose centre traverses a circle concentric with the world.
Theon is said to have constructed an orrery based on the model of Adrastus.
Duhem cites no other example of a philosopher using epicycles between Hipparchus and Ptolemy. Curiously, both Adrastus and Theon were peripatetics who justified the use of epicycles by arguing that they were the “accidental” consequence of the combination of the revolutionary and rotational movements of the planetary spheres.