You main Peach, so I can't give you a lot of the info that you'll need to successfully fight off an enemy without rolling consistently;
I know how I do it with Lucina and Lil Mac though. With Lucina, and especially Mac, I have mastered the art of spotdodging. Spotdodging, while sometimes in the same category of rolling, is a quicker and but more difficult to pull off way of avoiding damage. A spot Dodge can lead to a good counter if your good at foreseeing an attack. (For reference Spot-Dodging is the Shield+Down move also known as Sidestepping, ect). Mastering this can land some good openings to hip bump with peach or smash them with an uncharged golf-club. (Warning: Certain attacks can break through the spot dodging so it comes down to what attack you foresee).
Another good idea is to continue rolling, but initiating a Down Smash after rolling twice or thrice. Most characters have d-Smash moves that effect both sides of their immediate area so you can achieve one of two things, hitting the person in the front as a counter, or hitting the person in the back whom was dodge rolling to avoid a center attack. Either way you hit them, and its considered a good counter-offensive move.
Again, I can't really help you on specifics because I don't main peach, but... thats my Two cents.