The simplest thing would be to use a LFSR (linear feedback shift register) based pseudo random binary sequence generator (PRBS). This is done with a simple shift register with XOR feedback from a couple of taps in the shift register back to the input. Trigger the scope on the clock that is running the shift register, and the output of the shift register will be displayed as an eye diagram.
This can be built in hardware using logic chips such as a serial input shift register, a few XOR gates, and a oscillator. It can also be done with a micro platform such as an Arduino, and a bit of code to generate the clock and data signals on a pair of output pins.
Google PRBS generator, or LFSR circuit, etc. to get the details of some of the possible circuit configurations.