I think this is a great idea. It worked well in Singapore.
Singapore is an example of a country with a sterilization incentive program. In the 1980s, Singapore offered $5000 (US) to women who elected to be sterilized. Interestingly, the conditions associated with receiving this grant were fairly obvious in their aim at targeting low income and less educated parents. It specified that both parents should be below a specified educational level and that their combined income should not exceed $750 per month.[29] This program, among other birth control incentives and education programs, greatly reduced Singapore’s birth rate, female mortality rate, and infant mortality rate, while increasing family income, female participation in the labor force, and rise in educational attainment among other social benefits. These are the intended results of most incentivizing programs, although questions of their ethicality remain.