Anything other than a comparator with hysteresis would likely result is less than satisfactory operation. Hysteresis allows you to define a "dead zone" around the trigger point so that, if the voltage is wavering right around 3V it will not keep triggering on and off.
Here is a circuit:
R2 and R3 are a voltage divider that set the trigger point. In this case, 3V. You can replace them with a potentiometer to allow you to adjust the trigger point anywhere from 0V to 5V. Or, you can place a potentiometer between them, say 10K to allow you to adjust it over the range of about 2.5V to 3.5V.
R1 provides the hysteresis. In this case, it is about 2mV, so it triggers on the way up at 3.02V and on the way down at 2.98V. Make this resistor lower to increase the hysteresis, higher to decrease it.
L1 represents the relay coil. Depending on the relay you use, you may need to use a transistor to drive the coil.
The comparator is a random one built into LTSPICE. The LM339 is a popular widely available one that would work.
Bob