In early 1994, The Alvin Show aired on Nickelodeon under the title The Alvin Show on Nickelodeon until december 1995, when it was replaced by Alvin and the Chipmunks.
When The Alvin Show aired on Nickelodeon, there was an alternate version of the intro with Nickelodeon logos all over the background. Since The Alvin Show had a short-lived run on Nickelodeon, it's very rare and hard to find the Nickelodeon intro online.
A YouTube user under the name "Rugratskid4thaccount" had a lot of Alvin Show videos including the Nickelodeon intro, but around 2014, his account has been terminated due to copyright infringement and The Alvin Show on Nickelodeon intro has not been online since then, making it a lot more harder to find.
UPDATE: 4/25/17: I have found The Alvin Show on Nickelodeon intro on Vimeo. Link: https://vimeo.com/198593902