This is a question raised by a number of travels on limited time schedule hoping to visit gorillas in Rwanda on a single day tour plan. This is very much possible and best organized through a travel agency or can plan it your self, but would recommend booking through a travel agent as its more convenient. 
Your gorilla permit has to have been bought early enough as they get finished quickly.
A one-day gorilla trek requires the visitor to be in Kinigi by as early as 7 am which require the client to start the journey by 4:30 am in the morning and the journey is just about 2 and a half hour from Kigali to Volcanoes National Park. You require to drive in a 4*4 wheel to drive upto the trailhead where the briefing takes place. Though its also essential to overnight in Kinigi the night before the gorilla trek because a long nights rest is needed since some times the trek is strenuous, also you may get a strenuous gorilla group to track e.g. Susa can be far away and you could spend the best part of the day trekking. Plus people tend to want to head straight for a shower after the trek so that’s why you almost always do a 2-night stay around PNV. You could ask for a group near the park and if you got lucky, you could be back in Kigali that afternoon/evening. The trouble is if you don’t – the gorillas can move and make tracking time unpredictable
But yes, you can do it independently but it isn’t really done as a day trip from Kigali due to the factors outlined above e.g. early start (what if you get a flat tyre?), not assigned group until you’re there so no guarantee of a group nearby, if you get wet or have a tough trek, you probably would want to get showered and changed fairly quickly.
Yes clients can do a one day gorilla trip, after putting all the outlined risks in mind, and we have had many clients successfully track gorillas for one day at a very good deal in terms of cost.
A 1 day gorilla trek can cost about $1200 for a single traveller $1000 per person for group travelers price inclusive of gorilla permit, 4*4 safari van and an English speaking guide. This is very good deal for travelers with limited time but must track the breathtaking mountain gorillas.