Hot water with lemon juice in the morning before you eat. This really does work. Fresh squeezed lemon is better...but I have used lemon juice when I don't have lemons. Still works but maybe takes longer? I am not a coffee drinker, but there really is something about the hot water on an empty stomach that helps.
Hot tea and especially some of the herbal blends that have peppermint, spearmint or are labeled "dieter's tea" These are natural laxatives. Be careful with the dieter's kind...like a laxative you can get dependent on that one. For me, a mini 3 mint musketeers or mini York peppermint patty eaten before bed; followed up by the hot lemon water before breakfast works wonders. On my higher carb days I sometimes add in a Fiber One bar or brownie and crackers with fiber to my plan.
There is even yoga for constipation, some on youtube and other sites. Once I even watched a video for self-massage of the colon. I tried it using a little 5 lb medicine ball and it surprised me how well that worked! Low carb is well known for causing or exacerbating constipation; so I have done tons of google research on this.