As you mention most colored gases (Cl2, Br2, NO2, I2) are toxic and being a gas difficult to handle. Therefore not suitable for such demonstration. Maybe, you could try two small colored smoke bombs in a transparent container although the colour is not really a gas (more like fine particulate) in this case.
I would use liquids with the most common diffusion demonstration being a drop of blue ink in a glass of water. However, we need something fancier than that so how about this: Prepare a solution of red dye in water and a solution of blue dye and sugar or salt in water as well. In a 120 mL volumetric cylinder (needs to be large and for people to be able to see) add the sugar or salt blue solution and then on top of that layer with the red water solution by adding it slowly and carefully. Due to the larger density of the blue solution the two solutions will not mix instantly. You should end up with a bottom blue solution and a top red solution. Diffusion will start where the two liquids come in contact giving you a purple band in the middle which will expand over time with the speed being depending on the concentration of the bottom solution in sugar or salt (you ll need to tune this according to your presentation). You could even show how diffusion becomes faster with temperature by heating with a hairdryer but the effect will be masked a bit by convection.
This is how we grow crystals of compounds in the lab as well: Dissolve your compound in a heavy solvent such as DCM and layer it with a light solvent the compound doesnt dissolve in such as hexane. As the hexane slowly diffuses in the DCM solution the solubility slowly drops resulting in slow formation of high quality crystals suitable for X-Ray diffraction studies.