So I will admit I love rollercoasters, but I have convinced others who do not like them to go on Space Mountain with me many times. I always do the same thing with each person. I first always ask for the front seat to give to the new rider. While the ride is dark, you can still see generally what is going to happen if you are in the front seat. Also, I always say, the ride is primarily jerky turns and one "drop." Its a small drop but the speed and angle does cause the stomach in throat sensation sometimes. But this also can happen at one point during BTMRR, so if you can do that, you should be able to do this ride too. The "drop" is slightly after you fly through the area where your coaster originally gets pulled up at the beginning of the ride, so you can prepare yourself for it.
I hope you give it a try, everyone who I have brought on has gone on to ride many times more. The only person I know who does actually hate it, does not like riding because he feels he will hit his head as he is rather tall and the coaster seems to be a little low at times.