Any 'bold/deep/dark color is going to have an off taste
For red start with a *very dark/bright/deep* pink OR orange OR yellow. Then add some 'no taste' paste/gel color & UNsweetened KoolAid (such as black cherry or strawberry. This needs to be done at least 8-12 hours ahead of time so make it like the night before. In the am it might have some dark spots throught it but all you need to do is give it a good stir and they will disappear
Any paste or gel color that has 'super' as part of the color such as 'super pink' or 'super purple' etc will be stronger in color.
Another way if you only need a small amount is to buy one of Wilton's plastic tubes of red (Costs about $2.29). Cut the back off and scrape out the icing. Add that to about the same amount of your icing. It helps also if you use any of the colors mentioned above for red: pink, orange or yellow. Those tubes of colored icing are soooo very saturated w/color you can easily mix it and still have a nice red color. I also do this with blue, black and brown