For transesterification, please stir the KOH pellets with methanol thoroughly so that no KOH is left in it. Then pour this solution slowly and stir it continuously. For esterification, please add methanol first and stir it thoroughly. Then add acid catalyst. After biodiesel production, wash it with distilled water several times. During chemical water removal use higher amount of chemicals so that no water is left in the biodiesel. Hope, this will make the color light.

Treat your oil sample with activated charcoal ,activated bentonite clay or kaolin powder before the esterification , it will work for some extent

I used to run the methyl ester, trough a bentonite column. It was a vacuum filtration type of setup and the biodiesel diluted with hexanes or any other solvents you can easily remove after filtration. From safflower or castor oil you can get a clear almost colorless methyl ester.

If you apply this procedure on the crude product then later the water washing is a breeze...no problem with soap formation

Yes you can treat your biodiesel sample even after esterification with activated charcoal , activated bentonite clay or kaolin powder as well.

The reason your product is dark is because of your feedstock. CPO is usually refined, bleached and deodorized to give RBD oil which is more suitable for biodiesel production and will give you a higher quality biodiesel. Still you should not ignore the fact that CPO is a source for lots of other components such as carotin and vitamin E which are not necessary to be available in biodiesel. also now a days the concern of using food for energy production is an issue. Anyway if you want to have brighter biodiesel maybe you can use bleaching agents (clay) for the purpose. still your biodiesel quality will not be high. washing biodiesel can help to improve the properties as well.

Adsorbents mentioned in previous answers will give important decreasing in color, but the product will not be colourless.

If you really want colourless product, the most available way is the vacuum distillation which produces really colourless produc. , In this way you can fractionate your biodiesel into winter and summer type biodiesel.

About chemical/physical methods. It is worth to try oxidize/hydroxylize/butoxylize the biodiesel when the product properties will be improved and the color will be decreased much.

Adding CaO then cc. sulphuric acid (without water) in a small amount will give more reaction with the color components than with the main ester components. Epoxidation and treatment with butanol can decrease the color as well with improving the fuel properties.

• The color of a biodiesel depends on its feedstock (oil), and the oil is a mixture of various fatty acids such as Lauric acid (C12H24O2), Myristic acid (C14H28O2), Palmitic acid (C16H32O2), Stearic acid(C18H36O2), Oleic acid(C18H34O2), Linoleic acid(C18H32O2), etc.
• Biodiesel is a mixture of Fatty Acid Methyl (or Ethyl) Esters; referred as FAMEs (or FAEEs). Therefore, the basic color of a biodiesel depends on oil from which it is derived.
• Example: Coconut oil mainly consists 46-54% lauric acid (light yellow with fatty odor), 16-20% myristic acid (light yellow with sweet odor), 7-10% caprylic acid(colorless to pineapple color), and 5-8%capric acid (colorless). Therefore, the coconut biodiesel is clear, white to slightly yellowish in color.
• The safflower oil contains about 72-80% linoleic acid (pale to dark yellow) and 8-16% oleic acid (yellow to amber). Therefore, the color of safflower biodiesel varies from light yellow to dark yellow.
• The castor oil (or ricinus oil) has about 90% ricinoleic acid (C18H34O3), a hydroxy mono-unsaturated, 18-carbon fatty acid; (C18:1, cis-9,12-OH). Ricinoleic acid is colourless to yellow liquid. Therefore, the biodiesel obtained from castor oil varies from colorless to light yellow in color.
• The palm oil (derived from fruit) mainly consists of 38-44%palmitic acid(colorless), 21-25%linoleic acid(pale to dark yellow) and 20-24% oleic acid(yellow to amber). Therefore, the color of a palm (fruit) oil varies from light yellow to dark yellow. And after thorough washing and heating (to remove moisture), all the biodiesel fuels appears as crystal-clear (bright) liquids.
• The conclusion is "the color of a biodiesel fuel mainly depends on fatty acid composition of the raw oil from which it is derived".

TO improve the biodiesel color pass it through the plant/animal charcoal bed/coconut or rice bran husk, so that impurity will be adsorbed on it & color get improved.Distillation under reduced pressure will also improve the color.

You have to pass it through activated carbon.