Could you just give a little tinkly laugh and say something like, "Oh, [mum in law's name] I love your accent, it's lovely to hear it!" I think being very light about it but consistent is the way to go. It might not stop her immediately but hopefully will go some way to overcoming the insecurity over time.
I would just make a comment when she says stuff, like "oh he loves to hear your voice", "aww he can tell it's granny talking, he always smiles when he hears you", kinda thing. Or even "well me and ds think you have a lovely accent".
She's insecure about her accent, just make positive comments about it - try and bolster her self esteem a bit.
Background: I'm married with a six-month old son. I'm from the Home Counties; my husband is from the north east. I have an adulterated RP accent (the odd estuary sound); my husband lost his northern accent about ten years ago and, apart from the odd bath/grass/how way man you'd never know he was originally from there. My generally lovely mother-in-law, however, retains her lovely, native tones. The point is coming soon, I promise.
Right. Deep breath. Whenever she speaks to our baby, either in person or on Skype, she apologies for and criticises her accent e.g. "It's that funny woman again with the funny accent.", or, "you don't understand me because I talk all funny." I cringe every time I hear this, as, although he doesn't have a clue what's going on now, he will soon enough, and to my mind, the only reason for him to develop any anti-Geordie prejudices is if he is taught them by her, at least until he's much, much older and even then I'm not sure how and why that would happen.
How do I bring this up, and I think that I must (there isn't a cat's chance that my husband will - that's several threads I haven't the time or the energy to begin), without upsetting her? She's not terribly resilient, and has very recently lost her wonderful husband. Perfectly ready to be told to let it lie, but I feel now that I don't want my son to be taught that his father's family has a peculiar, or wrong, way of speaking.