I think that Coriakim may have waited for Lucy to come to take the spell off because: 

1.  To teach her a lesson 

If she didn't come to take the spell off, she never would've seen the book and may have still have that urging jealousy of Susan. She also would've never known the lesson of Eavesdropping that Aslan taught her after looking through the book. He was waiting for her to learn something, as with all things in Narnia. 

2.  To save her friends 

Lucy went to make the dufflepuds invisible because they threatened her friends. She made a deal with them saying that she would turn them visible again and they would not harm her friends. If Coriakim knew she was coming, he probably knew that she was in danger. If he made the Dufflepuds visible himself, the Dufflepuds would have no reason to spare Lucy or her friends. 

Convenient Plot Reasons, naturally. I love VDT, but I did notice last time I read it that it's very episodic and a number of the incidents are a little bit contrived, including the whole Magician's Book sequence. But it's such an enjoyable book and so beautifully written (as are all the Chronicles) that I didn't even notice that as a 7-year-old first-time reader and I certainly don't mind it even as an adult. It does give Lewis an excuse to have Lucy go off on her own (for the only time in this book) and have an adventure all to herself, in which we see her struggling with her jealousy of Susan and falling for the temptation to eavesdrop on her friends — all of which gives us something to think about as readers and dispels any illusions we may have had about Lucy being too perfect!

From an in-story point of view, Coriakin obviously had some foreknowledge of how the invisibility spell would be broken — here's what he tells Lucy:

"Well, of course I knew when I let the Duffers make themselves invisible that you would be coming along presently to take the spell off. I wasn't quite sure of the exact day. And I wasn't especially on the watch this morning. You see they had made me invisible too and being invisible always makes me so sleepy...." (p. 139 in the Puffin edition)

So although he did have the power to undo the spell himself, he clearly had no intention of doing so — it seems he knew it was meant to be that a girl from somewhere else would come and do it, presumably at the right time when the Duffers had learned enough of a lesson (if they could ever learn anything!).

It's clear enough from the way Coriakin talks with Aslan that he knows Aslan well, so perhaps it was Aslan who told Coriakin, or at least hinted to him, that Lucy would come to break the spell and so he (Coriakin) should leave the Duffers invisible until then. We don't know for sure, but it's fun to have it all kept a little mysterious. And we can assume Aslan meant for Lucy to learn a few lessons from her experience with the Magician's Book as well, which is why it all had to happen the way it did. As Shasta says of Aslan in HHB (p. 174), "he seems to be at the back of all the stories"...  

The monopods mention that only a young girl can cast the invisibility and visibility spells. Don't ask me why Aslan would give Coriakin spells he couldn't cast. To be honest, I'm not sure how the majority of the spells in his book would help to rule the monopods.  

Posted by: @col-klink

The monopods mention that only a young girl can cast the invisibility and visibility spells. Don't ask me why Aslan would give Coriakin spells he couldn't cast.

I was wondering that myself until just this morning when I went back to the book and found the actual quote from the Chief:

"... I say, my little girl she says the spell, for it's got to be a little girl or else the magician himself, if you see my meaning, for otherwise it won't work." (p. 121, emphasis added)

Posted by: @col-klink

To be honest, I'm not sure how the majority of the spells in his book would help to rule the monopods.

Neither am I... I've always wondered if the magic book had been around longer than Coriakin — that is, perhaps he inherited it from some earlier magician when he was sent to rule the Duffers (as a punishment for something he did when he was a star, which can't be disclosed to mere humans, as we learn from Ramandu). There's something about the magic book itself that gives me the feeling that it dates back many centuries and perhaps has been added to by different magicians as they learned or created spells for different needs. I can't think of anything in the narrative that gives us any real clues as to where it came from, unless there's something I've missed.

Posted by: @col-klink

The monopods mention that only a young girl can cast the invisibility and visibility spells. Don't ask me why Aslan would give Coriakin spells he couldn't cast. To be honest, I'm not sure how the majority of the spells in his book would help to rule the monopods.  

In fact, the original text says "for it's got to be a little girl or else the magician himself, if you see my meaning, for otherwise it won't work". So Coriakin could have done it himself.

Also, I was curious how did he know that Lucy would come? Did he have a vision or something?

I guess Coriakin had to stay on that island because of the mistake he made. But all of his powers were not taken away so he most likely had the power to make the Dufflepuds visible again from the very beginning. He might have chosen not to do it before the Dawn Treader arrived so that it would keep the Dufflepuds from becoming overly concerned about their appearance.  They didn’t end up being “uglified” when they did get their final appearance (in fact they looked quite nice).  I wonder why Aslan didn’t make them smarter, but some might see their foolishness as being cute, which may have added some appeal to the story.

@mickey That’s a good question. I’m sure it will be brought up on Into The Wardrobe Live on youtube. I think one theory might be that Coriakin himself was invisible, so he didn’t enough power to reverse it.