I think I know what the issue is...
First, take all your "songs" and place them on a single track, side by side.
second, put the song position pointer (the line that moves from left to right as the song progresses) at the start position of song 1.
third, open the lists group (in the right hand side of your arrange window, should be icons with names "notes, Lists, Media) and select Tempo.
4) select "create" and you should have a tempo marker. Play with the tempo number until your first song clicks are in time (you need to have the metronome on, the little icon on the bottom right hand side of the arrange window).
5, Move the song position pointer to the beginning of the second song,
Follow steps 2 to 4.
Repeat until you have as many tempo markers as songs. if you did it correctly, you should be able to play your Logic project from start to finish, and the click will match the correct tempo at the start of each song.
Make sure your "follow tempo" in not checked in the inspector of your audio track, or the song/region your trying to find the tempo on will stretch and shrink as you alter the tempo.
I hope that is what you are asking for, if not, I'm at a loss to help any more.
Good Luck,
FYI The thing you are trying to do with Logic does require some understanding of the basics of Logic and how it works with Tempo. I suggest you look into the chapter in the "Help" menu selection: Logic Pro Help: Logic Pro 9 User Manual: "Working with Tempo and Regions". it will enlighten you quite a bit in regards to what I think you are looking for.