If you think you dislike brown rice, you can use parboiled rice, which is more traditional in India. Just bump up the urad daal by another 1/2 cup. It's not that I use brown rice for health reasons. I deep fry things, thank you very much. It's that the flavour is (to me) far superior to white or parboiled rice. My sister and her husband flew in from India, and had dosa all the time. To tell me that mine is excellent is a pretty ringing endorsement.
To make it easy on me, I use the measuring cup that came with my rice cooker. I do four "cups" of brown rice, and wash it once. You don't want to wash off any of the natural/wild bacteria or yeast on the surface of the rice. Soak it for twelve hours in cold water. The next day, soak 1/4 "cup" (I like a lot of fenugreek, but it will make your dosas slightly bitter; feel free to scale back if you think you'll dislike it) of fenugreek seeds in water for 1 hour. Then, soak 1 "cup" urad daal in water for 30 minutes. The urad daal doesn't need very much soaking. When my mum bought a dosa grinder, the recipe that came with it suggested that she only soak the urad daal for a short time. So far, it's been working great.
SEPARATELY grind the urad daal, fenugreek, and rice, until it's very finely ground. Use the smallest amount of water humanly possible to lubricate. It's best if you use the soaking liquid. Here's the method I do. I strain out the soaking liquid for the urad daal, and set it aside. I add the soaked urad daal to the blender, and start it on low speed, along with about 1/4 of the liquid, to get it going. Once it's chopped up fairly well, I crank up the speed to high, and pour in more soaking liquid, as needed. When it's ground to a fine paste, I stop the machine, and dip my finger into it. I rub the dough between my fingers to ensure that there's no grit left. If there's no grit, I pour it out into a mixing bowl, and grind the fenugreek seeds the same way.
Once the fenugreek and urad daal are ground, I add the rice, 1 "cup" at a time, to the blender, along with 1/4 "cup" of the soaking liquid. Start it on low speed, and get the rice grains chopped up. Once they're good and chopped up, add a bit more water, and increase the speed to high. Keep adding water as needed, occasionally stopping the blender to scrape down the sides. Again, try to use the smallest amount of water you can possibly do. It's vitally important to grind down the rice very finely. Otherwise, your dosa will be gross. Also, the reason I'm asking you to grind the rice in such small batches is because you want the rice to get thoroughly ground, without overworking your motor. If you have a vita mix, feel free to use two to three "cups" of rice at once. It can handle it.
As you finish grinding the rice, pour it in with the ground urad daal and ground fenugreek. Finally, at the last batch, grind the rice along with a generous pinch of salt. Why? You want the dosa batter to ferment a bit, and it will, like a sourdough. Because of the fenugreek seeds and urad daal, you'll have a good fair bit of wild yeast in there, and it'll get nice and sour. The pinch of salt keeps the yeast from over-multiplying, and making your batter taste off. You don't want very much, because you don't want to kill the yeast. Just a nice pinch should do it.
Using a wire whisk, thoroughly mix together the ground rice, ground urad, and ground fenugreek. Cover with a kitchen towel, and let it rise in a warm~ish location. If it's cold out, feel free to wrap it in a few thick terry cloth towels, and set it near your radiator. If you don't have a radiator, preheat your oven to as low as it'll go, and turn off the heat. Wait about 1 minute, and put the mixing bowl in there. It'll rise just fine now.
Let it rise while you're off at work. If you time this just so, you can soak the batter before you sleep, grind the batter the next morning (budget at least an hour if you don't have a powerful blender, like a vita mix), and let it rise while you're at work. Anywhere from 8 - 10 hours later, your dosa batter will have puffed to double the size. It'll smell very like sourdough, and make you hungry. Don't cook it yet.
For the best results, I give everything a very good stir, and put it into the fridge overnight, to let the rice and the rest fully rehydrate. I don't know why, but for whatever reason, that final park in the fridge just makes it work. When I don't park it in the fridge overnight, it tends to make a mess of my pans, and not turn out properly.
The next morning, pull about 1 1/2 cups of dosa batter, and add just enough water so that it's like a crepe batter. Whisk it with the extra water very well. The dosa batter will keep for a good week or two. I'm not sure exactly how long it'll keep, because we tend to go through it in a couple of days. Cook up your dosa, and enjoy with salt, vegetables, or coconut chatni. :)
UPDATE: As of late, I've been making smaller batches of dosa batter at home. To make sure that my tiny little blender can handle it, I sprout the brown rice, which seems to make it softer. To sprout brown rice, wash it once under hot tap water. Soak it in more hot tap water, covered, in a place where it won't be disturbed. The next morning, drain off the water, and rinse the rice under lots of cold running water. Place the drained, washed brown rice into a tupperware container, and put it into your fridge for one more day. It will be perfectly softened 24 hours after you drain and rinse it.
Once you have sprouted your brown rice, you can also cook it much more quickly than if you used raw brown rice. In my rice cooker, I can set sprouted brown rice for "white rice" setting, and it cooks to perfection.