None of the above are correct. Correct is: Do come and visit this coming holiday. Do not say "please" here. It sounds ridiculous. There is no 's' on 'holiday'.

Yes, use "during". And use "holiday" (singular), unless you are refering to more than one holiday or celebration.

Well, "this coming holiday seems little awkward" INstead in my opinion the correct sentence would be " Please come and visit me during these coming holidays" Its my opinion, not the final word..! So, anyone is welcomed to make a correction in it..!

Please, come and visit me during this coming holidays. The usage of "during" is better because it shows the length of the visit you want the visitor to stay. The word "holiday" should go in the plural form as it is common to travel for a couple of days, not only one.