For pully and mopsy, a list of things to help with sleepy babies...
make sure your free hand is supporting your breast so the weight of the breast isn't on the baby's chin
switch breasts as soon as the baby begins to lose interest in active nursing, this may need to be done every 30 to 60 seconds at first (the first few times you do it).
Burp and change nappy. Burping should be done with the baby sitting supported upright on mom's knee or lap rather than over the shoulder because it's also less sleep-inducing.
nurse in clutch or "football" hold as opposed to cradle hold - it's a little less "cuddly" and sleep-inducing.
massage the baby's head (crown) in a circular motion while nursing. Also using a wet cold washcloth and wiping back against the grain of the hair growth can help.
Place baby on your lap with legs near your tummy and head on your knees.
Gently supporting baby, raise in sitting position, like doing a "sit- up". Do this two or three times, then do "side to side" a couple times.
You can also try breast compression.
It is worth remembering that these are rescue measures and that a couple of days of using these ideas to get as much milk into your babies as possible is all it will take to get them to be more awake.