Consider your subject matter. What type of instrumental track will serve your rap best? If you've got a soft, emotional lyric in mind, think about writing something soulful. The beat you write needs to be solid, but consider something besides a drum for the emphasis. A tambourine on the downbeat might be more appropriate, or an electronic bass and a click track. If your subject is more about anger, write a harder rhythm. Always make the music track fit the mood.
Compose melody and musical fills with a variety of sounds. Write a funk guitar line with a slap and pop bass underneath, then add short musical phrases intermittently throughout. The key is to leave a lot of space for the rap itself. The music should create a good foundation, but you don't want distracting musical sounds going on that will take away from the lyrics.
Change the rhythm and beat, which are essential, part of the way through the instrumental track. There's nothing wrong with going from a traditional hard-hitting beat to a soft, more melodic approach that allows a rapper to sing. The combination of the hard rap verse followed by a soulful rhythm and blues chorus adds color to a piece.
Experiment with different sounds. A lot of rap is composed on electronic keyboards that feature sounds you can't get from any other instrument. Take advantage of these sounds. Add special effects to add texture to an instrumental rap. This helps to keep the sometimes repetitive beats from becoming stale.
Consider purchasing basic music beats. There are several professional websites that sell original beats which you can use as a basis for your songs. You may also want to consider sampling, which is basically taking a portion, or sample, of another song or a sound, and using it as the foundation of your beat. Typically, raw samples are processed and rearranged to fit the needs of your particular beat, and the end result may or may not closely resemble the original sample.
Use a music writing or sequencing program on your computer. There are many programs available that you can use to write basic beats and add instrumentation. With some practice, you can create your own instrumental raps.