local songs = {
    "http://www.roblox.com/asset/?id=2538961789",
    "http://www.roblox.com/asset/?id=4867633321",
    "http://www.roblox.com/asset/?id=2231782710",
    "http://www.roblox.com/asset/?id=2206587324"
}
local songLength = #songs               
local Sound = script.Parent.Parent.Sound    
local CD = script.Parent                                             
local selected = 0                      
CD.MouseClick:Connect(function()            
    selected += 1                       
    local chosen = selected%#songs      
    if chosen == 0 then                 
        chosen = #songs
    end
    print(chosen)
    Sound.SoundId = songs[chosen]       
    Sound:Play()--playing the song
    end)

Your script is way to long.
And it has lots of errors.
I think this.

local music = Instance.new("Sound") -- music variable

local button = script.Parent -- the button

local clickDectector = button.ClickDectector -- the buttons click dectector

clickDectector.MouseClick:Connect(function() -- when the player clicks


local sound1id = "put number"

 local sound2id = "put number"

 local sound3id = "put number"

 local sound4id = "put number"

--Custom settings
music.Volume =   1   -- Number here
music.SoundId = sound1id
-- plays the music
music:Play()
-- when it ends
while wait(0) do
wait(music.TimeLength)
music.SoundId = sound2id
music:Play()
wait(music.TimeLength)
music.SoundId = sound3id
music:Play()
wait(music.TimeLength)
music.SoundId = sound4id
music:Play()
end
end)

~~~~~~~~~~~~~~~~~

This could use a lot of cleaning up and shortening

though it seems like you have an understanding of everything you used so I wont go over each thing. First lets get this loop working. It seems like you want it to wait till the end of each song, so lets do that first.

Song cycle

Using the sound.Ended event you can check if the sound ended:

sound.Ended:Connect(function()
    -- play next song --
end)

event:Connect(function()) is functionally the same as function yourFunction just all on one line.

Now we can create a table with all of your sound ids/urls in it.

local songs = {1234567, 7654321, 1325476}

{} constructs a table out of the provided values

Now we can use the code we made before and combine them.

local songs = {1234567, 7654321, 1325476}

sound.Ended:Connect(function()
    sound.SoundId = songs[]
end)

[] should contain a number of which value in the table the script will use

We'll need something to iterate through the table and clip it when it reaches the limit.

local songs = {1234567, 7654321, 1325476}

local iteration = 1

sound.Ended:Connect(function()
    sound.SoundId = songs[iteration]
    iteration = iteration + 1
    if iteration >= #songs then
        iteration = 1
    end
end)

# tells you how many values are in a table

Finally add sound:Play

local songs = {1234567, 7654321, 1325476}

local iteration = 1

sound.Ended:Connect(function()
    sound.SoundId = songs[iteration]
    iteration = iteration + 1
    if iteration >= #songs then
        iteration = 1
    end
    sound:Play()
end)

Now that we covered that lets do the

Click detection

This part is mostly the same, just instead of using sound.Ended we use clickdetector.MouseClick

clickdetector.MouseClick:Connect(function()
    sound.SoundId = songs[iteration]
    iteration = iteration + 1
    if iteration >= #songs then
        iteration = 1
    end
    sound:Play()
end)

Now we squish these two scripts together and:

local songs = {1234567, 7654321, 1325476}

local iteration = 1

sound.Ended:Connect(function()
    sound.SoundId = songs[iteration]
    iteration = iteration + 1
    if iteration >= #songs then
        iteration = 1
    end
    sound:Play()
end)

clickdetector.MouseClick:Connect(function()
    sound.SoundId = songs[iteration]
    iteration = iteration + 1
    if iteration >= #songs then
        iteration = 1
    end
    sound:Play()
end)

Though even still this could be shorter, instead of repeating all that code we can just use a function.

local songs = {1234567, 7654321, 1325476}

local iteration = 1

function iterateSong()
    sound.SoundId = songs[iteration]
    iteration = iteration + 1
    if iteration >= #songs then
        iteration = 1
    end
    sound:Play()
end

sound.Ended:Connect(function()
    iterateSong()
end)

clickdetector.MouseClick:Connect(function()
    iterateSong()
end)

And finally were done, hope this helped!

This can be done much more efficiently:

local song1 = "http://www.roblox.com/asset/?id=2538961789" --paste wanted song ID
local   song2 = "http://www.roblox.com/asset/?id=4867633321"
local   song3 = "http://www.roblox.com/asset/?id=2231782710"
local   song4 = "http://www.roblox.com/asset/?id=2206587324"     

local soundblock = Instance.new("Sound")
soundblock.Name = Music
soundblock.Parent = script.Parent
soundblock.Looped = true
soundblock.Playing = false
local songqueue = 1

local function PlayMusic()
soundblock.Playing = true
songqueue = songqueue + 1
    if songqueue > 4 then
    songqueue = 1
end
button.ClickDetector.MouseClick:connect(PlayMusic)

while true do
    if songqueue == 1 then
        soundblock.SoundId = song1
    else if songqueue == 2 then
        soundblock.SoundId = song2
    else if songqueue == 3 then
        soundblock.SoundId = song3
    else if songqueue == 4 then
        soundblock.SoundId = song4
    else soundblock.SoundId = song1
            end
        end
    wait()
end