Rechargeable Gameboy Color modification
Without a schematic or more data about the gameboy circuits it is not possible to say if it is absolutely safe.

From the images on that page the resistor seems \$1\Omega\$ 1W, while the diode seems a jellybean 3A rectifier, like the 1N5408 or similar.

EDIT
(following the OP posting a link to the schematic)

I don't see any particular issue, save the possibility of overheating. The charger circuit is extremely rudimentary (a diode with a limiting resistor in series). Assuming the rechargeable cells are of NiMH type, they would require at least a constant current recharging circuit (sophisticated chargers also monitor the voltage and the temperature of the cell during charging). The cells could be well run the risk of being overcharged and get damaged. During charging you should watch out for any excessive temperature rise of the cells. Moreover, never leave the GBC under charge unattended. 

Make sure that the cells' chemistry IS NOT lithium-based (I don't think it is, but you never know). Overcharging lithium-based accumulators is very dangerous, they may explode and take fire!