The charisma skill is a big help, just say hello to twenty five people and then you get a nice boost but it reset each town so I had to repeat that, when her charisma skill got higher I found she made friends much quicker, it was certainly worth the time taken to learn it.
I always had mum ask people their career then you can usually 'enthuse about...' whatever it was for a double plus, if you were lucky you might find out they were a workaholic then you could 'praise hard work' for another double plus, a lot of traits give you a certain 'enthuse about...' social that is a double plus so what I did was rotate between any of those I'd discovered plus the career one and add in a get to know or tell dramatic story in between so they didn't get bored, also those two help you to discover more traits which might give you even more to enthuse about.
I mainly targeted people in certain career outfits, medical, culinary, military and law enforcement as they were most likely to have extra traits like workaholic, genius, natural cook and athletic all good for double plus socials.
Sometimes I got lucky with a sim who also had dislikes children and a kid being on the lot, then I could have mum gripe about kids to them