A carriage ride is romantic, calming, and just beautiful when you are with the person you love! So the idea to propose on a carriage ride will be great! You can arrange a carriage ride by surprising her during the day or evening.
It would be nice to arrange this when the weather is nice and you don't have to worry about the rain, or cold weather. You can propose to her while the carriage is going or have it stop at a particular spot that you think she will find special and propose to her there.
Again, you can make the proposal public, by inviting friends and family to show up at that special spot to witness the proposal, or you can make it more private and keep it for just the two of you. You can have this proposal videotaped by a friend or professional and have it as a keepsake forever.