How to to test the concentration of melatonin in a strong acid?
Is there any relatively simple method to determine the concentration?


That depends on your equipment. Having the following at hand would be helpful:


a UV/VIS spectrometer
mortar and pestle
UV-grade ethanol (or methanol)
pure melatonin


How to proceed:


Prepare a stock solution of the pure melatonin in ethanol.
Prepare some dilutions for the expected concentration range.
Measure the UV absorption of all solutions at $\lambda = \pu{277 nm}$.
Draw your calibration curve (absorption vs concentration).
Powderize the tablet using a mortar an a pestle.
Dissolve the powder in a defined volume of ethanol. 
Measure the UV absorption of the sample.
Determine the concentration in the sample using your calibration curve.


You have just applied the Lambert-Beer law. Others have done the same and reported the method in Pharmacophore 2014, 5, 252-257 (free PDF).