Carrier doping effects on spin dynamics in Sr(14-x)A(x)Cu(24)O(41) (A=Ca, Y, and La) are investigated by Cu NMR and NQR. The energy gaps in the spin excitation spectra (spin gap) are confirmed to be Delta=140 K for the CuO2 chain and Delta=470 K for the Cu2O3 ladder in Sr14Cu24O41. The spin gap for the ladder increases with the Y and La substitutions for Sr (up to x=3), while it decreases with increasing x in Sr14-xCaxCu24O41 and seems to collapse around x=13 of the Ca substitution. Hole-doping effects on the spin gaps for the ladder configuration an interpreted in terms of magnon and hole-depairing excitations for the spin S=1/2 ladder.