It is important to understand that the "rasp" you're looking for is caused by a distortion of sound created by imperfectly resonating vocal chords. Most vocalists work to economize and improve the efficiency and elasticity of their vocal chords; thus increasing their range and making their tone more pure.
Thus, most everything that you can do to increase this distortion would be to cause damage to your vocal chords. This is very important to consider because if done often for a long period of time, it can cause permanent vocal chord damage, and then you wouldn't be able to sing at all.
You are absolutely right that coffee can affect your voice - just as milk, soda, or juice. The preferred drink before singing is water since it is the healthiest for you.
I will do my best to offer suggestions that are the least-damaging to you. The first suggestion I have for you would be to sing normally and then have the audio engineer alter the timbre of your voice to have a more raspy quality.
Alternatively, it is relatively easy to make your voice more aspirate sounding by pushing more air through your vocal chords than you would use to make sound. To do that, start by singing a pitch, and then try and transition to just breathing outward; doing it as smoothly as you can. A breathy, aspirate sound will lie somewhere in between.
Lastly, you could try taking a drink of water; swallowing nearly all of it, but leaving a few drops in the back of your throat. This can help increase the distortion of pure sound by influencing the vibration of your vocal folds.
Try not to do it for a long time, too often, or too loudly. If you sing quietly the audio engineer should have no problem turning up the signal on your mic to compensate.
Also remember that your voice will deepen and become more raspy as you age; as your vocal chords lose elasticity, so anything you do now is going to be amplified when you're old. You ever see the commercials for Men's Warehouse? Imagine him when he's in his late 70's.
Hope that helps.