In order to use a copyrighted animation/drawing/etc of Wile E. Coyote you would need to contact the original artist. If you wish to use the trademarked character you will need to contact the registrant Warner Bros. Entertainment Inc.
You will need identify the rights holder and compose an email/fax/snail mail that should include at least these elements...
1) Identify yourself
2) Identify the work you want to use
3) Describe...