  By introducing the shape invariant Lie algebra spanned by the SUSY ladder
operators plus the unity operator, a new basis is presented for the quantum
treatment of the one-dimensional Morse potential. In this discrete, complete
orthonormal set, which we call the pseudo number states, the Morse Hamiltonian
is tridiagonal. By using this basis we construct coherent states algebraically
for the Morse potential, in a close analogy with the harmonic oscillator. We
also show that there exists an unitary displacement operator creating these
coherent states from the ground state. We show that our coherent states form a
continuous and overcomplete set of states. They coincide with a class of states
constructed earlier by Nieto and Simmons by using the coordinate
representation. \pacs{3.65.Fd, 02.20.Sv, 42.50.-p}
