I have build a circuit to drive the solenoid valve and a small DC water pump both operates at 12 volts dc.
Before I connect these 2 loads to the circuit the working of relay and is perfectly working fine, but as soon as I connect these 2 loads relay is getting chattered.
Circuit and relay is operating at 5volts DC and load is 12 volts.
I'm a little confused where you're getting the 5V from, but generally inductive loads (relays, motors) can cause quite large negative spikes on their power supply. I suspect this may have something to do with your problem.