Most of us feel sleepy on the rainy day. Different people have different views about this aspect. This sleepiness may be because of the production of serotonin in our body in the dark rainy days are low. Serotonin is regulated by sunlight which effects mood.
Also the production of melatonin is increased in the dark i.e. in the rainy day. It is produced by a gland in the brain known as pineal gland. Scientists say that its formation is less in the sunlight and hence we didn’t feel much sleepy on a clear day as compared to the rainy day.
One reason for this could be that moisture gives relaxation to our body like we feel much relaxed after the shower Also the rhythm raindrops falling on the earth. The pleasant climate decrease in our daily activities. Increase of quietness and stillness and the mental caress that we get from rain lead us to feel sleepy on the cool rainy day.
I think you place far too much emphasis on the “sunlight” factor.
It fails to take into account that the place we “see” the greatest effect of rain-relaxation is in places where there is already very little sunlight. Schools, Hospitals, etc.
People feel sleepy because the weather becomes cooler, and not to mention gloomier. Look at it as if things start to wind down making one feel calmer. On a more humourous note, one knows that raining means no outdoor activity and so sleep .