I love Weissbluth's book and have been following it since around 6 months when I finally had the sense to read it and understand how/why children sleep the way they do. I cannot say enough good things about it. JG has some fantastic advice; mine is fairly similar.
Our son is now 15 months and about 6 weeks ago, started showing signs of 'nap dropping readiness'. Prior to that, he would wake each day around 6:00 - 7:00, take his first nap from 9:00 - 10:30/11:00, take his second nap from 1:00 - 3:00/3:30, then go to bed around 6:30. He was so predictable and would fall asleep and stay asleep without issue.
Just before 14 months, he would still take his morning nap and then refuse to take his afternoon nap or have a hard time getting settled down for it. Sometimes he would skip it altogether. As you can imagine, it made for a pretty rough afternoon because he was exhausted. On those days, I put him to bed earlier - sometimes at 6:00 or even 5:45. My son has some pretty strong "please put me to sleep" cues (he gets clumsy, whiny, cries for me to pick him up but then wiggles and fusses out of my arms), so whenever he presents these cues I respect them and put him to sleep.
We tried making the morning nap shorter in hopes that he'd still want his afternoon nap. It didn't work. What we have done is try to keep him awake and entertained during the morning to 'hold him off' so that he only takes an afternoon nap. It works when we schedule new, fun, different activities that hold his attention. It did not work when we used to do our usual routine (which would be wake, eat, go downstairs and play) because he would want to go to sleep again by 9:00...mostly because that was what he was used to. At daycare this has been really easy - he transitioned to the toddler room where everyone naps at the same time. On the weekends, I actually schedule new and different things to keep him entertained and draw his focus away from the old schedule. This past weekend, we did breakfast at our normal time, played for a little bit, then went to watch a volleyball tournament. He had a blast and must have forgotten that "hey I usually nap at 9:00". I've never felt like he is sleep deprived because he is not showing the 'sleep cues' at his typical naptime of 9:00 nor is he falling asleep. But, boy, when it is time for the afternoon nap he is out like a light and could sleep for 3 - 3 1/2 hours!
This could take several weeks, but you could try to either make the morning nap short (no more than an hour) or make the 'morning nap' the only nap but just gradually keep pushing it later and later each day. The hard part about pushing the nap later is that you'll be on a goofy schedule but keep in mind it is only temporary. Your baby may want to go to bed at night a little earlier than normal but don't panic because in our experience we found that an earlier bedtime has not equalled an earlier wake time; in fact he sleeps a little bit longer in the morning. As a result, he is more well-rested and can make it through the morning without the nap.
I thought I would miss the days when our baby took two naps but to be honest, I'm thrilled that he showed signs of wanting only one nap and took to the transition like a champ. I don't feel like our day is so constricted now, and we can actually get out and do more fun things with the baby!
Good luck to you and feel free to PM me with questions. I'm no expert, but I totally love Weissbluth's methods and am fortunate to have had a great deal of success with them.