Karen:
I concurr on feeding excessively sleepy newborns by fingerfeeding with a
syringe and tube.  I find that babies can be fed this way while they continue
to sleep.  I would be afraid of using any other method of feeding a sleeping
infant, for fear or triggering aspiration, apnea, bradycardia, whatever; but
with a syringe you can really control the milk flow.  Often they have just
gotten into a vicious cycle of hunger and weakness, leading to inability to
suck effectively, leading to greater weakness.  A few calories delivered this
way gives them the needed energy to get their next meal on their own, at the
breast.
        Catherine Watson Genna, IBCLC