You can do that using ARB_texture_env_combine and NV_texture_env_combine4/ATI_texture_env_combine3 (depending on what hardware you use, of course).
Set first combiner to modulate primary color and texture color.
glTexEnvi(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_COMBINE);
glTexEnvi(GL_TEXTURE_ENV, GL_COMBINE_RGB, GL_MODULATE);
glTexEnvi(GL_TEXTURE_ENV, GL_SOURCE0_RGB, GL_PRIMARY_COLOR);
glTexEnvi(GL_TEXTURE_ENV, GL_SOURCE1_RGB, GL_TEXTURE);
Set the second combiner to modulate primary alpha and texture color, and then add to previous result.
glTexEnvi(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_COMBINE4_NV);
glTexEnvi(GL_TEXTURE_ENV, GL_COMBINE_RGB, GL_ADD);
glTexEnvi(GL_TEXTURE_ENV, GL_SOURCE0_RGB, GL_PRIMARY_COLOR);
glTexEnvi(GL_TEXTURE_ENV, GL_OPERAND0_RGB, GL_SRC_ALPHA);
glTexEnvi(GL_TEXTURE_ENV, GL_SOURCE1_RGB, GL_TEXTURE);
glTexEnvi(GL_TEXTURE_ENV, GL_SOURCE2_RGB, GL_PREVIOUS);
glTexEnvi(GL_TEXTURE_ENV, GL_SOURCE3_RGB, GL_ONE);
or
glTexEnvi(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_COMBINE);
glTexEnvi(GL_TEXTURE_ENV, GL_COMBINE_RGB, GL_MODULATE_ADD_ATI);
glTexEnvi(GL_TEXTURE_ENV, GL_SOURCE0_RGB, GL_PRIMARY_COLOR);
glTexEnvi(GL_TEXTURE_ENV, GL_OPERAND0_RGB, GL_SRC_ALPHA);
glTexEnvi(GL_TEXTURE_ENV, GL_SOURCE1_RGB, GL_PREIVOUS);
glTexEnvi(GL_TEXTURE_ENV, GL_SOURCE2_RGB, GL_TEXTURE);
Treat this as pseudo-code. Check the extension specifications for more information.