I was in the same hurdle you were, going from Coban to Livingston and this is the fastest, comfortable and cheapest option: At around 7 am every morning, there is a bus terminal I don't quite remember the name but it's just 3 blocks away from the Coban cathedral downtown that has the earliest bus to Guatemala City, you just buy the ticket that leaves you at the halfway point called "El Rancho", the ticket costs about 80 quetzales or something.
The bus leaves around 7:30 am on the nice and smooth highway and it doesn't have a lot of passengers or stops so you can just snooze for a while. Around 9 am the bus will stop you in front of a lame looking cafeteria in the highway just 5 minutes away from the bus terminal of El Rancho. Unlike buses in Mexico where you can stay in the bus and keep sleeping, Guatemalan buses literally kick everyone out which kind of sucks and you are stuck outside the parking lot of the cafeteria for 20 minutes. I guess you can go buy something to eat at the place but most of the food is horrendous, at least the toilet facilities are free though. I probably find the cafeteria deal to be uber annoying because the Rancho terminal is just 7 minutes away. I find it annoying that I have to be stranded for 20 minutes when I could have arrived at the terminal by now. You are warned.
You will arrive at the El Rancho terminal at 09:30 am, the buses that take you to Rio Dulce leave at 10:30 am so you could either just sit there watching cable tv on their screen or carry all of your luggage and walk around the village. El Rancho is a boring dusty village with no Maya, the only reason I'd think anyone would go explore it was to eat some tacos in a street stand or something.
The 10:30 am Rio Dulce bus is punctual and leaves at around 10:45 am, it has a few bus stops they have to make and yet another enjoyable 20 minute cafeteria stop at the halfway point near the highway deviation to Zacapa, yaaay more expensive bad food and 20 minutes sitting in a parking lot in the heat! Expect to arrive at Rio Dulce at 4:30 pm, too late to get to Livingston. The bus ticket costs about another 80 Q. You can still get to Livingston that night if you opt to take a bus to Puerto Barrios instead of Rio Dulce which has more regular schedules. If you arrive to Puerto Barrios at 5 pm you might still get a chance to catch a late boat ferry to Livingston. I wouldn't suggest staying in Puerto Barrios for long, it doesn't look like a very safe place at night.
You can take the street buses from Coban to El Estor, but since there is no shiny and nice highway it will be a miserable bumpy ride in crowded Chicken buses. There is apparently a nice highway that connects Flores-El Estor which some say is a faster route (however remember that it's a 5 hour detour from Coban to Flores).
If time is a huge issue, you can try to find a way to hire a shuttle from Coban to Rio Dulce but it usually won't fill up with enough passengers and they will probably end up dumping you at El Rancho bus terminal for much more money than taking the bus I suggested above. You will end up arriving to Rio Dulce at 4:30 pm and spent twice as much money doing so, but if you woke up at 8:30 am I guess it's an option.
Oh, one word of advice: The boat shuttles from Rio Dulce-Livingston and viceversa are tourist oriented. It's a great trip and they will show you the outside of San Felipe Castle and a bunch of swampy islands filled with birds, but it's a 3 hour ride.. everytime. Even the locals that need a ferry to a halfway point are kind of stuck seeing bird island for the zillionth time. I took the 1:30 pm shuttle boat from Rio Dulce.