  This paper is a direct illustration of a construction of coherent states
which has been recently proposed by two of us (JPG and JK). We have chosen the
example of a particle trapped in an infinite square-well and also in
P\"oschl-Teller potentials of the trigonometric type. In the construction of
the corresponding coherent states, we take advantage of the simplicity of the
solutions, which ultimately stems from the fact they share a common SU(1,1)
symmetry \`a la Barut--Girardello. Many properties of these states are then
studied, both from mathematical and from physical points of view.
