I've heard that the Jin are the first people that used cannon to defend Kaifeng when attacked by the Mongols.
So did the cannon successfully repel the Mongols?
From Cambridge History of China Vol 6: Alien Regimes and Border States 907- 1368
"The siege of Kaifeng is also of some interest for the history of
military technology, because gunpowder was used by both parties, if
not as propellant for projectiles, then certainly for grenades hurled
by catapults.These bombs were used by the defenders of Kaifeng against
men and horses, with deadly results. Another weapon credited to the
inventiveness of Chinese artisans was a flamethrower ( or rocket?),
called a "fire lance." Sixteen layers of strong yellow paper were
pasted together and formed into a pipe over sixty centimeters long.
This pipe was filled with a mixture of charcoal made from willow wood,
iron fillings, powdered procelain, sulphur, and niter and was fastened
to a lance.The soldiers handling these weapons carred a small iron box
with glowing embers and, in battle, ignited the fire lances, which
ejected a flame over three meters long. When the explosive were spent,
the pipes could be reloaded."
So to answer your question, some types of gunpowder weapons were used, but no cannon. The siege was ultimately successful and on 29 May 1233 the city gates were opened to the Subetei. The last Jin emperor escaped to Caizhou and committed suicide next year during a Mongol-Sung siege.
However, I've also heard that one of the disputes between Kubilai Khan and Sung is that Kaifeng was captured by Sung.
The Sung did try to recover their historical capitals of Kaifeng and Luoyang in 1234 but were easily repulsed by their "ally", the Mongols. The Sung never seriously considered recovering their northern territory. The final conquest of Sung by Kublai Khan was in 1279. I'm sure those incidents provided very good excuses for the Mongol to attack Sung.