You should search for Melanin Content assay.

Briefly:

The melanin content following agent treatment can be measured as described previously by Hosoi et al and Yoo et al. with slight modifications {*Links are attached*}. Briefly, melanoma cells, normal human melanocytes or human fibroblast cells will be grown in 6-well culture plates until they reach 70-80% confluency. The cells will be exposed to various concentrations of tested agents or controls for XX hours. At the end of the treatments the culture medium will be collected and centrifuged at 1200g for 10 min. The extracellular (secreted) melanin content can be determined by measuring the absorbance of the collected medium at a wavelength of 405 nm. On the other hand, cells will be washed with PBS, trypsinized and collected in 1.5 mL microcentrifuge tubes; and lysed with 500μl of 1 N NaOH containing 10% DMSO next will be incubated at 80°C for 1 hour. The absorbance at 405/475 nm will be measured via a microplate reader. The absorbance of fibroblasts (non-pigmented cells) will be used as background and subtracted from the readings. The melanin content can be determined from a standard curve prepared from a standard of synthetic melanin (Sigma, USA). In a replicate set, cells can be collected for protein determination using BCA protein assay (for normalization purposes) (Pierce, Rockford, IL).

http://www.ncbi.nlm.nih.gov/pubmed/?term=21810462

http://link.springer.com/article/10.1007%2FBF02931083

You should search for Melanin Content assay.

Briefly:

The melanin content following agent treatment can be measured as described previously by Hosoi et al and Yoo et al. with slight modifications {*Links are attached*}. Briefly, melanoma cells, normal human melanocytes or human fibroblast cells will be grown in 6-well culture plates until they reach 70-80% confluency. The cells will be exposed to various concentrations of tested agents or controls for XX hours. At the end of the treatments the culture medium will be collected and centrifuged at 1200g for 10 min. The extracellular (secreted) melanin content can be determined by measuring the absorbance of the collected medium at a wavelength of 405 nm. On the other hand, cells will be washed with PBS, trypsinized and collected in 1.5 mL microcentrifuge tubes; and lysed with 500μl of 1 N NaOH containing 10% DMSO next will be incubated at 80°C for 1 hour. The absorbance at 405/475 nm will be measured via a microplate reader. The absorbance of fibroblasts (non-pigmented cells) will be used as background and subtracted from the readings. The melanin content can be determined from a standard curve prepared from a standard of synthetic melanin (Sigma, USA). In a replicate set, cells can be collected for protein determination using BCA protein assay (for normalization purposes) (Pierce, Rockford, IL).

http://www.ncbi.nlm.nih.gov/pubmed/?term=21810462

http://link.springer.com/article/10.1007%2FBF02931083

Alternative assays: Tyrosinase activity assay.

Briefly, normal human melanocyte cells and pigmented mouse B16F10 melanoma cells should be grown in  6-well culture plates and treated with increasing concentrations oftested agents or controls  for XXX hours.  Next, cells will be washed with PBS, trypsinized and collected in 1.5 mL microcentrifuge tubes.  20 mM Tris/HCl (pH 7.5) buffer containing 0.1% Triton X-100 will be used to homogenize cells and tyrosinase activity (oxidation of L-DOPA to DOPAchrome) will be monitored as following.  Cell extracts (50 μl) will be mixed with 100 μl of freshly prepared substrate solution (0.1% L-DOPA in phosphate-buffered saline @ 37 °C).  The production of DOPAchrome will be monitored by measuring the kinetics of absorbance at 475 nm (for 20 min every 30 seconds). Data will be corrected for auto-oxidation of L-DOPA and the slopes of the kinetic readings will be calculated to determine and compare tyrosinase activity.  

Alternative Approach 2: Assessment of melanin transfer from normal human skin melanocytes to keratinocytes following agent treatment.  In mammalian skin, melanin is synthesized in melanosomes of the melanocytes and then transferred to the keratinocyte cells through release into extracellular spaces followed by endocytosis by keratinocyte cells.  This process can be investigated by a flow cytometry based melanosome transfer assay will be used as described previously. Please check the links

http://www.ncbi.nlm.nih.gov/pubmed/?term=18702635

http://www.ncbi.nlm.nih.gov/pubmed/?term=22363165

For your information, in addition to all the correct information from Omer Faruk Kuzu, melanin can be quantitatively estimated without any interference from cell debris etc using the chemical methods developed by Ito and Wakamatsu. Basically, it consists in an oxidative degradation with permanganate/hydrogen peroxide (eumelanin) or HI (pheomelanin) and the HPLC determination of some marker units formed in the degradation . It is tedious but all interferences are avoided. I am also involved in a new technique for melanin determination using Raman, but this is not developed for secreted melanin in cell culture media. Look at recent literature for details about these techniques.