There are a couple of rental spots you can check out.
These three outfitters have some great ideas and packages if you like. Outer Limits and Free Wheeling specialize in touring but also have bikes for rent, while MacQueen's is a bike shop that will rent out bikes and help organize excursions. All three have good reputations and are very easy to work with.
The Confederation Trail is very easy to get to from Charlottetown, but if you want to go further afield the above outfitters can help with that as well; from renting bike rack for your car to actually shuttling you to and from particular points on the trail.
I hope you have a great time exploring our little island!