In rain, it is best (safer) to stick with the relatively flat trails. The reason is that many of more vertical trails include stretches of going up (or coming down) over bare granite, which can become slippery in the rain. I suggest that your first stop in the park be at the Hulls Cove visitor center. Check out the big 3-D model to get a feeling of what the topography looks like for various trails.
One system of good rainy-day trails is the Jesup Path/Hemlock Road/Wild Garden group that runs from the Loop Road through the edge of Great Meadow, past Sieur de Monts, and out to The Tarn and back. It is a rough figure-8 route and one of the all-season favorites of local residents.
As I noted in a response to someone else recently, the problem with most weather forecasts around here is that they are developed for an area that stretches from the coast north to Bangor (ca. 45 miles away). For a more specific forecast for MDI, take a look at: