So, in this scenario, people are living in an Earth-sized planet, with an atmosphere. They travel via ultrafast train that carries them to the solid core of the planet, where they then transfer to other lines that take them back to the surface. However, an issue is that in the deeper parts of the tunnel, air gets denser and denser as there's more air pushing down, and I'd prefer to not have hundreds of airlocks. How else might I simply solve this?
Just have your ultrafast trains travel in a vacuum. When a train docks at a station, airtight connections will allow passengers to get on or off. When the train is ready to go, the connections will be closed and withdraw, leaving the train in a vacuum tube.
This will also allow your trains to travel much faster - with no air in the tubes, there will be very little friction, and you don't have to worry about the shockwaves you get when you approach the speed of sound.
Now you only have to worry about keeping the air in the central station fresh. However, seeing as you have the technology to send trains to the center of the planet, keeping air fresh should be a fairly simple task.