In addition to walks in the stroller, she can put the baby down in a swing or on a blanket aimed so he can see her for 20-40 minutes while she's on the treadmill, in front of the exercise DVD, on her mini tramp to music, etc. If he cries, she should just keep going, or she won't get the job done. Or do it when he's napping. I get it, she wants to use the exercise to bond, but bottom line, she won't get a good workout. When my kids "climb on me" while I do my floor work or yoga, I let them for a minute, but then I really need to get the work done. She should do bonding exercise in addition to real exercise-not instead of. He'll be OK, sounds like he needs a little confidence building by some brief absences and learning momma always comes back and she isn't controlled by crying-this could get worse later if she doesn't set him down long enough to exercise.
I remember coming in from long jogs with the baby stroller, putting my daughter in her crib, and doing all my sit ups right where she could look at me. She would sometimes cry, but once she knew the routine, she would settle in her usual viewing spot and watch and even laugh. She loved it.
Your friend needs her health and stamina and he WILL be OK, and he'll get used to seeing her do it. She can do some baby sit ups for fun etc, but again, put him down long enough to do a real regime of 3 sets of 15 each for good resistance muscle exercises for core, legs and arms. Or a DVD that includes these. Careful not to blame the baby for not exercising, and good for her that she is looking at ways to do it.
My gym was $400/yr during a holiday special and I locked in the price-it has daycare with a one way window where I can see them at all times and the kids love going and I get a proper 2 hr workout-keep your eye out for specials if you ever have the budget. It's NOT fancy-I hate it, the music is awful, but it has saved my health these past 3 years. It ends up being faster to just got there than to try to do videos etc while tending to all the kids.
Good luck to her and she can spend the rest of the day bonding-her son will be happy if she feels happy and energized, she'll have more energy to play with him!