Not sure about Taiwan but should work for Mongolia, their population is tiny and they are fairly poor. Offer each household $100,000 one time payment to agree to annexation. Number of households is ~1 million, one time cost of $100 billion (Chinese GDP is now >$20 trillion and Chinese net national worth is >$100 trillion). Will pay itself back very quickly anyway.
(Outer) Mongolians have their national identity, and much of it is based on their hatred of Qing. It's not just Chinese that has national pride.