Addendum to `Gravitational Geons in 1+1 Dimensions'

In a recent paper [arXiv:0807.0611] I found gravitational geons in two classes of 1+1 dimensional theories of gravity. In this paper I examine these theories, with the possibility of a cosmological constant, and find strong field gravitational geons. In the spacetimes in [arXiv:0807.0611] a test particle that is reflected from the origin suffers a discontinuity in $d^2t/d\tau^2$. The geons found in this paper do not suffer from this problem.