A very dear friend of mine cares for her mother of 95 in her home alone.
The last three months I have offered many times to help with more tasks about the home, supply transportation to and from doctor, shopping etc. She tells me that she can handle it all on her own, and doesn't want to trouble me.
AKAlicious said it so well. Maybe you can even invite them to your house for dinner. They might like that.
I think saying your thoughts out loud to your friend might help. By that I mean saying things like:
"I'm not sure what to say to let you know how much I want to help you with this huge job you have."
"I don't mean to bug you but I know if I were caring for my mom I would just have to have someone to help. I want to be the friend to you that I would want if I were in your shoes."
"I know that if I were doing this for my loved one you would help me, please let me do something, anything for you."
"I care about you so much and I want to show it by joining you in this path that you are taking."
"I don't mean to make you feel like you aren't doing a FANTASTIC job because you are, I just want to be in your life and right now this is your life. Please let me be a part of your life!"
Again, DON'T GIVE UP!
Please tell your friend how awesome she is and how much you admire her and how much her mom surely appreciates her. And I say the same to you. You and your friend are both wonderful women!
Make a small basket with a few treats, some magazines, a book, all occasion cards or assortment of cards and stamps.
Or bring over breakfast or lunch with all the plates napkins, drinks, etc and spend some real time with her and her mother, maybe play a card game or scrabble together...or just visit. It will be so appreciated when you just take the initiative to plan and take the decision making off her. Certainly call the night before and tell her your plan.
It's hard for others to ask for or accept help, but kind gestures are always appreciated. Isolation for caregivers is so common and difficult as they watch friends move on or enjoy activities they can't schedule.
Good luck and let us know what works.