A quick survey of possible sources suggests that cash handouts are rare but that it is very common for "benefits in kind" (such as free food, education, healthcare or travel), to be distributed only to those recipients who are prepared to convert (or to say that they have converted) to the donor organisation's preferred religion.
In some cases (food, healthcare) the recipients are in a position where their lives, or those of their families, may be in jeopardy if they choose to maintain their existing religion and are thus denied access to the resources they need to live.
Here are some of the sources I looked at:
Imagine you’re poor and living in a rural area. Your child gets sick. You manage to transport her to a hospital or clinic. To your relief, the condition is treatable. But the cost of treatment is not just beyond your means, it’s beyond your imagining. However, says the kindly health care worker, you can get the treatment free of charge. All you have to do is renounce the centuries-old traditions of your people and convert to a foreign religion.
Such offers are being made to desperate people in the villages and tribal areas of India.
Missionaries in India: Conversion or Coercion?, Philip Goldberg, Huffington Post 19 Feb 2014
I have a personal experience of evangelical groups trying to convert members of my family. Two house maids who converted said that the school where their children went raised fees and due to their inability to pay, they were told they would waive it if they converted (which they were forced to do). Of course, the school was rabid in their evangelism with these children. I use a taxi company for travel over the last ten years. I have noticed over 30% of drivers have converted over the last 5 years.
When asked, inevitably they spoke about evangelicals groups that gave them free education for children and paid their medical bills, provided they converted.
Conversion: With targets & incentives, new breed of evangelical groups are like start-ups, TV Mohandas Pai, Economic Times (Times of India), 27 December 2014
To put this in a broader context, the World Council of Churches (WCC) working with the Pontifical Council for Interreligious Dialogue (PCID) and the World Evangelical Alliance (WEA) has 'Recommendations for Conduct' which condemn this kind of coercion:
A basis for Christian witness: 6. If Christians engage in inappropriate methods of exercising mission by resorting to deception and coercive means, they betray the gospel and may cause suffering to others. Such departures call for repentance ...
Acts of service and justice. ... Acts of service, such as providing education, health care, relief services and acts of justice and advocacy are an integral part of witnessing to the gospel. The exploitation of situations of poverty and need has no place in Christian outreach. Christians should denounce and refrain from offering all forms of allurements, including financial incentives and rewards, in their acts of service.
Discernment in ministries of healing. As an integral part of their witness to
the gospel, Christians exercise ministries of healing. They are called to exercise
discernment as they carry out these ministries, fully respecting human dignity
and ensuring that the vulnerability of people and their need for healing are not
Christian Witness in a Multi-Religious World: Recommendations for Conduct, World Council of Churches / Pontifical Council for Interreligious Dialogue / World Evangelical Alliance, January 2011 (emphasis mine)
There is a tension between humanitarian aid and proselytisation which the Red Cross has tried to address:
The 1995 Red Cross Code of Conduct ... governs the
activities of non-governmental humanitarian agencies responding to both
natural and man-made humanitarian crises. Significantly, four of the
eight sponsors of the Code are faith-based agencies while four are secular,
symbolising the concrete nexus between faith-based and secular discourse
in the context of humanitarian intervention. The Code places obligations
on faith-based humanitarian agencies and on the secular-minded donors
that provide much of their funding. Faith groups are enjoined to provide
humanitarian aid in an impartial or non-discriminatory manner, ie on
the basis of need and not creed. Parties commit that “We will not tie the
promise, delivery or distribution of assistance to the embracing or acceptance
of a particular political or religious creed.” Significantly, however,
the Code does not prohibit the use of aid in furthering the proselytising
objectives of organisations that combine evangelism, ie spreading the
word of God and seeking converts to the faith, with humanitarian service.
Religion and development: Challenges for donors and for faith groups, Gerard Clarke, Department of Political and Cultural Studies, Swansea University, UK (emphasis mine)