So, I can't speak to all the possibilities/option.... I know there are many different agencies.
However, PADI, in my opinion has a good e-learning option. Google PADI. Check out the e-learning for open water diving certification. You will still need pool and open water dives. But, the e-learning process will accelerate everything.
You should be able to complete everything, at a reputable center, in a weekend. Some pointers:
1. if do e-learning, you get access to the course for 12 months. so go through it a few times to get real familiar.... and especially re-review before whatever weekend you are going to do your certifying training/dives/etc....
2. However you choose to do your training, look for reputable training center that has their own boats. There are plenty that have good charter contracts.... and I am not knocking them. But, the best situation is a training center that owns their own boat/s cause they can adapt the schedule and really customize according to the divers.
3. Where ever you go for your certifying training, make sure the cost they quote is COMPLETE. That is, no hidden additional fees. You want the all included costs. You do not want to fly somewhere, pay your course costs... then find out there is a boat surcharge or certification filing fee or some other "hidden cost".
4. I have been biased to Florida for over 30 years.
All that said, I love diving and encourage anyone and everyone to consider it. It is definitely do-able and really a good thing to share with a friend, significant other, child or even a stranger you meet on the boat to buddy dive!