How can I increase the output current to make it sufficient for relay module?
The relay module requires a 5V powersupply to operate.  Simply switching the inputs will not operate the relays with out that 5V power source.

You do not need R12 for your TSR1-2450 switching regulator. It can handle loads up to 1 ampere and input voltage up to 36V.
You don't need D4.  It is redundant. D3 is all you need as a reverse polarity protection.
C3 and C4 are optional as the 2450 includes them.  You only need C3 if the input voltage is above 32V.


Install jumpers in place of R12 and D4.
Remove R11 entirely.
C3 and C4 can stay, just make sure they are rated for the proper voltage. (More than 24V for C3, more then 5V for C4.)

Outside of that, your schematic is incomplete.

You show no ground connections to the external world, though they must be present for the circuit to work.
You don't show the 5V connection to the relay module, although you seem to be trying to power the relay module from the 5V regulator.
You don't have bypass capacitors on the processor's power pins.  It may behave irratically. (Random lockups, doing odd things, etc.)
The reset pin is left floating.  That can cause random resets of the processor,or it could stay stuck in reset and not do any thing at all.

You don't need to add a ULN2803 to drive the relays.  All you need to do is to properly connect and use what you already have.

Your transistor input buffers are odd.  Most folks would wire them as inverters.  Pull up to 5V on the collector, emitter to ground, a resistor from the base to the signal input.  Connect the collector to the processor's IO pin.  It inverts the logic level, but that doesn't really matter.