Theres a few things to try to see if things can be done. First thing first, go to the offending site and see if they have a way to contact the authour/webmaster - maybe a contact link or an email. In my experience, about half of websites will remove your tunes at your request when you just email them and politely ask them to do so in a non threatening manner. An example template I use is this;
Give it a week or two to get a reply. If the website has no contact function or your polite email has received no response after some time, then all is not lost - we just need to step up a gear. Time to do some investigation. Is the site hosted on something like blogger.com? go to the blogger.com helpdesk and notify them.Dear Sir/Madam,
Your website at <address here> is offering pirated copies of my works for download. I kindly request you remove links to my works from your site as you are distributing them without my permission. Im a small artist and dont make very much money from my works and in order to keep producing I need all the financial support I can get.
Some example URLs of my works are
http://their.site.com/path/to/mp3.1.mp3
http://their.site.com/path/to/mp3.2.mp3
(etc)
Please let me know when you have removed my copyrighted works from your site.
Kind Regards
<you>
If its not, go here and put in the sites name without the http or path (eg 'google.com' instead of 'http://google.com/search'). You want to search for type 'A' and click resolve. You will then get a response which should have something like this at the bottom
some.site.com. A 2400 83.123.123.123
You now know that the site hosting your material is on IP 83.123.123.123. But what use is this? Lots - we now try to find out where this IP is located and who owns it. Go again to http://www.dnswatch.info/ and select the 'location' tool. Put in the IP address you got before to find out where exactly in the world your pirate material is being hosted. Ive just found out that the site im looking at is located in the USA.
If the pirate material is located on a server in the USA you have a massive advantage - the DMCA takedown notice. If its not, dont fret most companies will work with you once you tell them a customer of theirs is hosting pirated material and damaging their good corporate image. You also have the added benefit that servers IP/s located outside of the USA may be owned by a USA parent company so they tend to respond to DMCA takedowns. I have in the past had fasthosts in the UK respond to USA style DMCA takedowns.
So now we need to know who owns that IP address in order to talk to them. Go here and put in the IP address you have. It will return a long list of text, search for 'abuse' and you will see an email address. This is who we are going to talk to next.
If the IP is located in the USA, then send a DMCA takedown notice. A template is
A US based server *MUST* reply to a DMCA takedown notice and remove your works. Normally they will email their customer and if they get no reply within 4 days, they just turn their whole server off. OoopsSubject: DMCA Takedown notice
Dear <name of ISP>,
I am the copyright owner of the works hosted on your servers at:
http://www.host.com/path/to/file
http://www.host.com/path/to/file
http://www.host.com/path/to/file
(LIST ALL OF THE URLS YOU CAN FIND TO ALL OF YOUR WORKS, THEY ONLY HAVE TO REMOVE ONES YOU SPECIFY)
This letter is official notification under the provisions of Section 512(c) of the Digital Millennium Copyright Act (“DMCA”) to effect removal of the above-reported infringements. I request that you immediately issue a cancellation message as specified in RFC 1036 for the specified postings and prevent the infringer, who is identified by its Web address, from posting the infringing works to your servers in the future. Please be advised that law requires you, as a service provider, to “expeditiously remove or disable access to” the infringing works upon receiving this notice. Noncompliance may result in a loss of immunity for liability under the DMCA.
I have a good faith belief that use of the material in the manner complained of here is not authorized by me, the copyright holder, or the law. The information provided here is accurate to the best of my knowledge. I swear under penalty of perjury that I am the copyright holder.
Please send me a email response indicating the actions you have taken to resolve this matter.
Kind Regards

If the server is outside of the USA, something like this usually works;
In 90% of cases where the original website owner didnt get back to you, one of these two emails should result in the content being removed from their servers. Ive used this method time and time again and it tends to work.Subject: Piracy on your servers
Dear <name of ISP>,
I am the copyright owner of the works hosted on your servers at:
http://www.host.com/path/to/file
http://www.host.com/path/to/file
http://www.host.com/path/to/file
(LIST ALL OF THE URLS YOU CAN FIND TO ALL OF YOUR WORKS)
I kindly request that you remove all unauthorised copies of my works from your servers, identified by the web addresses in this email. Can you also let me know how you intend to prevent your customer from posting copyrighted works (with a view to assisting copyright infringement) to your servers in the future. I am a small artist and piracy is really hurting my ability to continue producing. Id therefore very much appreciate your help in resolving this matter. Im sure your company is not one that wishes to be associated with piracy and that your terms and conditions require your customers to own/have rights to distribute any content they publish via your servers or your network.
I have a good faith belief that use of the material in the manner complained of here is not authorized by me, the copyright holder, or the law. The information provided here is accurate to the best of my knowledge. I swear that I am the copyright holder of the works available via the links specified above.
Please can you send me a reply to this email address outlining any steps you will be taking to remove the links to my copyrighted works, or if you do not intend to remove the copyrighted works your justification for doing so.
Kind Regards
I wont say this method is iron clad and it is clearly time intensive. Worth it tho imho. One less link to a full tune is more potential sales.
I hope it helps you.