Answer: Most evergreens with umbrella shapes will grow much larger than 10' so you may want to consider growing a shrub such as a viburnum and training it into a tree shape instead. Of those evergreen trees with umbrella shapes, these are the smallest:
Dwarf southern magnolia Magnolia grandiflora 'Little Gem' -- smallest; slow growing; Sweet bay magnolia Magnolia virginiana Tolerates wet soil; Japanese red pine Pinus densiflora 'Umbraculifera' -- dwarf, umbrella-shaped.
It's nearly impossible to keep rabbits from eating your grass, unless, of course you fence your yard. Wish I had better news for you!
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