  A class of noncanonical effective potentials is introduced allowing stable,
radially symmetric, solutions to first order Bogomol'nyi equations for a real
scalar field in a fixed spacetime background. This class of effective
potentials generalizes those found previously by Bazeia, Menezes, and Menezes
[Phys.Rev.Lett. 91 (2003) 241601] for radially symmetric defects in a flat
spacetime. Use is made of the "on-shell method" introduced by Atmaja and
Ramadhan [Phys.Rev.D 90 (2014) 10, 105009] of reducing the second order
equation of motion to a first order one, along with a constraint equation. This
method and class of potentials admits radially symmetric, stable solutions for
four dimensional static, radially symmetric spacetimes. Stability against
radial fluctuations is established with a modified version of Derrick's
theorem, along with demonstrating that the radial stress vanishes. Several
examples of scalar field configurations are given.
