Different music contains different vibrational energy. Im not going to get all technical about vibrations and soundwaves.. what it does to our own energy...blah blah blah. Just short and sweet: music is awesome and demons love it.
When deciding what to offer a companion or a DL with regards to music, the best way is to ask them what they like. This however, is not always doable as many of us do not have the "hearing" skills fully developed yet. Thats ok, dont worry, Im going to tell you how to figure it out without hearing.
Offering Music to a Companion
Think about your companion. What are their personalities like? The scrolls you get from S&S priestesses are usually very detailed as to their likes, suggested offerings, personalities etc. Read this over and spend some time meditating with them. You may just find that you get impressions, hear lyrics, get actual songs or bands. you can write down any impressions you may have.
Next , take yourself to your music player or youtube. start experimenting with different music. You'll know when you hit paydirt. You will feel an energy shift, a temperature change, a sudden peace, chills, or even an upswing in mood. This is your companion telling you "yes, this one!" Your Companion will LOVE the effort you are putting in to finding them something nice to listen to and it can strengthen the bond between you.
My Hellborn DC D likes hard, heavy balls to the wall metal. He loves the black metal sounds of Behemoth, Belial and Dimmu Borgir. I have to say this would not have been my first choice to listen to but when I offered something in my comfort zone- Metallica, he laughed and told me to get some taste in music

Offering Music to Dark Lords
The way you find out what a particular DL likes is very similar to finding out how you did with your companion. Read as much as you can on the dark lord. Whether it be through forums, personal experiences of others, groups that discuss that DL or dare i say it- a book. You can get a "profile" of that DL in this manner. You wouldnt offer Unsere, the gentle motherly Dark Lady who specializes in nurturing, fertility and comfort something like Behemoth or Dimmu Borgir now would you? lol No, she is much softer, less aggressive so you would naturally look in that direction. For Her, strange as it may sound, I find acapella is something She enjoys. She loves the fact that the "music" is made with just voices. the energies of the ones singing it, in harmony with one another allows the positive, musical energy to flow and she feels uplifted listening to it. Again, I was never a huge fan of Acapella myself but through Her, I learned to appreciate and enjoy the marvels of the human voice, what it is capable of, and how those energies can translate over into a magickal working during ritual.
However you explore with your music, just make sure that you keep yourself open, even to genres you wouldnt normally even look at. The journey is half the fun, but the reward of finding something your companion or DL loves is where the real reward is at!