Hello, Jeff.

Your question gets asked in various iterations by so many people! The simple answer is that there are no completely rabbit-proof perennials or shrubs. A hungry animal will eat just about anything, even plants that are labeled rabbit-resistant or deer-resistant. Fencing is the most effective option for keeping unwanted creatures away from your plants/garden beds, but that is not the most visually attractive option for most people. Though some repellants can work, they need to be reapplied after precipitation and rotated due to the tolerance animals develop toward products. 

That said, this list of plants from Penn State and Rutgers Extension has some shade species that might work for your garden beds. On the latter pages, check out the categories of plants “rarely damaged” or “seldom damaged” for some choices. 

You might consider using the Plant Elements of Design tool from the University of Minnesota Extension Yard & Garden team. Instructions help you complete each box, and you should get some options to suit your conditions.

Checking the area for places where rabbits might dwell (under decks, for example) and eliminating those conditions/access is another thing to help minimize their presence.

Sources:

https://franklin.osu.edu/sites/franklin/files/imce/Program_Pages/ANR/wildliferesistantplantlist.pdf

https://plantsearch.extension.umn.edu/searchplants/list?orderby=aCommonName

https://extension.umn.edu/news/keeping-animals-out-your-garden

Sincerely,

Julie