The Stuka was not an ideal platform for air to air combat. RAF test pilot Eric Brown's report on the Ju 87 is instructive on this matter:

The Ju 87D was big enough and slow enough to present an ideal target to the humblest tyro among fighter pilots and it must even have come high in the popularity stakes with anti-aircraft gunners. Certainly its large ailerons failed to instill any liveliness into evasive maneuvers, and although its elevators were reasonably light the aircraft was just too stable longitudinally to be very maneuverable.

The Ju 87 was a relatively large aircraft compared to other single-engined types and the flight characteristics needed to make it a good dive bomber worked against its air-to-air capabilities. The stability of the aircraft was necessary to place bombs accurately so throwing the plane around in a dogfight was not an option, especially since maneuvers denuded the rear gunner of his effectiveness. The Stuka was a single-purpose machine that made it unsuitable for many other roles.

That said, there were examples of Stuka pilots being awarded credit for air to air kills. Among Hans-Ulrich Rudel claims was that he shot down several Soviet planes. While most of these kills were in FW 190s, Rudel claimed to have shot down an IL-2 with his 37-mm cannon in his Ju 87G. Rudel's record is suspect both because of he was something of a creation of Nazi propaganda after the tide had turned on the Eastern front, so there was no reliable way to verify his claims, and he was a noxious blowhard in the postwar period that used his war record to embellish his neonazi politics. The 37-mm kill is certainly plausible- the IL-2 was as large and maneuverable as a Stuka while 37-mm autocannon could shred an aircraft if it hit it- but it is unverified. There were other claims as well; the Hungarian 102/2 Stuka squadron claimed to have shot down two La-5s and a P-39 in operations around Poltova in 1943, although these may have been rear-gunner kills.

Arguably the most interesting Ju 87 victory, and one that is confirmed, was that of Frank Neubert of I./StG 2 on 1 September 1939. Neubert was part of the first wave of Luftwaffe attacks on Poland and his flight attacked a Polish airfield outside of Krakow in the early dawn hours. After dropping his bomb-load, Neubert noticed a PZL P.11C scrambling to intercept the Germans. Neubert managed to take advantage of his advantage in altitude to shoot down the leader of the Polish flight, Captain Mieczysław Medwecki. This kill showcases a number of facets of Ju 87 aerial kills. One, the Ju 87 pilot needed not only surprise, but also other factors like altitude or speed advantages to be successful. It also helped a Stuka pilot if he had no bombs which further ate into the plane's already poor maneuverability. Finally, Clausewitzian chaos and happenstance had to play into a Stuka pilot's hands in order for an enemy aircraft to enter into his cone of fire of his wing guns.

The Neubert victory was also the first documented aerial kill of the Second World War. But this was very much the exception rather than the rule for Stuka pilots; Neubert engaged the PZLs because of a unique constellation of circumstances aligned. Most Stuka pilots knew their plane was no dogfighter and that engaging an enemy plane made it even more vulnerable. Even aggressive Stuka pilots would not court a dogfight as it was a plane very much unsuited for this type of combat.

Sources

Brown, Eric. Wings of the Luftwaffe. Ottringham: Hikoki, 2010

Weal, John A. Junkers Ju 87: Stukageschwader 1937-41. London: Osprey Pub, 1997.

_. Junkers Ju 87: Stukageschwader of the Russian Front. Oxford: Osprey Pub, 2008.