Depending on liner availability and the size of your rink you may find yourself in a position that you need to join two sheets of liner together.  Many in the BackyardRink realm do this and have great success with it.

Here is what I know from reading what others have done...

You need to make sure to seal the seam as tight as paoosible.  This can be done with several products.  Some of which are as follows:

Acoustical sealant

Roof Tar

Hot glue

Duct tape

From what I have read it is a combination of one of the first three in the list above finished off with the Duct tape.  I know I have tried to locate acoustical sealant, but did not have much luck.  Roof tar and hot glue are very readily available.  I myself use roof tar and white duct tape to seal leaks in the liner after water has been added, so from a certain point of view I can speak on the reliability of roof tar and duct tape.  The combination worked prefectly for me and sealed the leaks with very little issues afterwards.

One of the Yahoo group members has a tree inside his rink and has to cut and reseam the liner to get around the tree and i believe he used the hot glue and duct tape method for his and he does this year after year with no major failures.

As already stated it is extremely critical that you get enough sealant/tar/glue between the sheets that you ensure a water tight seal.  The addition of the duct tape helps seal and also keeps the sheets in place while you continue down the seam.