Doesn't sound like a trade or business to me, but then we don't have all the facts and circumstances.  

The circumstances are that they flew round trip to Mexico twice and stayed for a few months each time, they own their home in the US, in Massachusetts, and rented it out while they were away, they will return to MA, they don't intend to move to Mexico. In addition to the stipend their room and board in Mexico is provided. They don't receive a W-2 or 1099 for the stipend. They can declare their travel expenses if the stipend income is considered self-employment.

This is not a trade or business income. 

this is what the IRS considers a business. Link. https://www.irs.gov/charities-non-profits/definition-of-trade-or-business

The term trade or business generally includes any activity carried on for the production of income from selling goods or performing services. It is not limited to integrated aggregates of assets, activities, and goodwill that comprise businesses for purposes of certain other provisions of the Internal Revenue Code. Activities of producing or distributing goods or performing services from which gross income is derived do not lose their identity as trades or businesses merely because they are carried on within a larger framework of other activities that may, or may not, be related to the organization's exempt purposes.

You said your clients are volunteering, so it would not be a business for self employment.

Thanks everyone - So the stipend income is taxable but doesn't count as self-employment, is that right?

See this link from IRS, also research pub 17.

https://www.irs.gov/pub/irs-utl/oc_aug_volunteers_pay_taxes_072911_02.pdf