The Economist has a piece that discusses the advantages of diaspora bonds to poor countries. It notes:
The idea is simple. Poor-country governments can issue bonds and market them to emigrants in rich countries. There are several advantages to milking members of a diaspora. They are often patriotic: they like the idea that their savings will pay for bridges and clinics at home. They are patient, since they have a long-term tie to the issuer. They are less jittery than other investors, too, since they have friends who can tell them whether political unrest is really as bloody as it looks on television. And they are sanguine about currency risk. …
The idea of diaspora bonds is not new to India. The State Bank of India made a high profile issuance of the Resurgent India Bonds over a decade ago to non-resident Indians (NRIs). These have also been the subject matter of analysis (e.g., a law review article, and an economic study).
However, as the Economist article notes, there are obstacles to the utilization of these instruments by sovereigns, and not all diaspora bond offerings have been successful. See also a World Bank Blog on Diaspora Bonds.