Talk positively about the joy of saving up for something. I feel like that is something we have lost in the era of credit cards.
Budgets are awesome, but often unrealistic without first tracking spending for 2-3 months. We see it here on the board all of the time with people who are thinking about retiring.
Some of the spending tracking phone apps might be appealing to them, but even just writing each thing down can make you even more mindful of what you are spending. I would first ask if anyone does that, and then encourage them to try it.
If you go the budget route, make sure you start by giving them examples with numbers that are a realistic budget for a single mom . . . reasonable amounts spent on food, baby items, rent, utilities, car expenses/gas/insurance, shoes, taxes, phone, internet, etc. Otherwise, some of them will say their utilities are only $20 a month, or that they only need $100/month per food. They can count WIC or SNAP to cover some of their food budget if they have those benefits, but a food budget of $0 even if you have that benefit is unrealistic. My own family routinely spends around $1600 a month for food . . . that is more than $500 per person. It is shocking to me, but that is what we spend.