Can I use copyrighted material if I give credit?
Under most licenses, absolutely not. There are licenses that allow use which include creative commons licenses, as Mr Beast stated in his answer.
Can I use copyrighted material?
If you obtain a license to do so. This can be done by contacting the copyright owner, or abiding by the license that currently exists for the work, such as the case of a CC license.
You can also use such material if it falls under fair use. In your case, it probably does not, but doing research on it might provide more insight into fair use precedent. However, if you decide to pursue this route, know that this is decided on a case-by-case basis. In court. Contacting the copyright owner is much simpler.
Are there other options?
Yes, actually. As IMX answered, despite the downvotes on his/her answer, cover versions are not covered by copyright law in the same manner. You don't need owner permission, but you will need to pay royalties to the owner through a mechanical license.
Please note that, with the exclusion of fair use, all the answers involve a license in some manner. Mechanical licenses, contacting owners to license, utilizing the current license. There is no answer (beyond fair use, which is very limited and probably not useful in your situation) in which you can use a work without a license.