I recently made this 'lamp' using 5 simple circuits and red LEDs.
See it in action here.
1. Newton's Cradle of this style
2. 5 CR2032 3V Batteries*
3. Copper Tape
4. Conductive Thread
5. 5 Diffused LEDs of your choice
* You could also change up the circuit to use less batteries
Step 1: Wrapping the Lines
Use the conductive thread to wrap each of the lines from the support bar on one side down to each ball.
Step 2: Taping the Connections
First, fold the copper tape over itself to make flaps under the balls that make contact when they are in their stationary positions. From there, tape the cathode (negative) side of the LED to the flap, with the positive side facing the opposite direction. Underneath the anodes (positive), tape a strip going from either side of the support as shown. The batteries will fit in between the anodes and this strip.
Step 3: Insert Batteries
Insert the CR2032 batteries under each of the LED anodes to complete each of the circuits. You may need to angle them a bit to get a good connection. From there, the LEDs should light up and you should be ready to go!