Sending Analog Data with and IR LED
Seems to me you first need to establish a protocol.  Could just be a simple one you make up,  with it you will eventually find that repetition and retransmission will need to be explored, and you may want to include things such as a CRC if the application suits it; or not...

As part of the thought process you need to look at your sensors, see how they put out their data, you seem to indicate analog, so that would be read on an a to d converter and that d value might be directly sent as the data part of your chosen protocol.

Or some joysticks packages might have have a I2C or SPI driver built in to which the A to D wouldn't be required.

But using IR you will find timing and validation very important so that the receiver knows where the beginning and end of data is at.

Thinking about it there must some libraries out there already.
Or entirely completed projects to study.

Now you didn't ask but if reliable communication is desired you might want to go wired serial or use a managed protocol like an Ethernet peripheral.