To be honest, I'd say the main barriers to Romany Zionism are education and money.
If you can identify an articulate, educated, charismatic group of Romanies sometime in the C19th who would be willing to spearhead such a movement, you'd maybe have something to work with. However, I genuinely can't think of any - and I'm guessing that university educated Romanies in the C19th were few and far between, and more likely to downplay their Romany identity than fight on its behalf.
European Jews, by comparison, were generally well educated, articulate and often had access to the sort of capital which made political lobbying feasible. They also have a unifying religion, and a coherent national story which holds true across borders.
It's two very, very different cultures you'd be dealing with. National consciousness and the sort of motivations that gave rise to Zionism only really work in an educated context. Romanies simply don't have that context to refer to in the C19th and unless you create that, you can't have a Romany homeland.
Supposing, however, that such an educated, actively nationalist Romany middle class did exist, probably somewhere in Austria-Hungary: you then have to get them to agree that a homeland is the way to go. Many will be assimilationists; many will simply favour concentrating in certain districts of countries like Romania which already have substantial populations of Romanies.
If they can amass the wealth necessary to start lobbying governments, however, their emigrationist message would be well received in countries where gypsies have traditionally been identified as a problem population. In much the same way as the Liberians were 'helped' to emigrate by the states who hosted them, Europe's Romanies could find themselves pushed as much as they are pulled. Often, the pushing won't be pleasant. I could see the Austrians, Romanians, Serbs and Hungarians willing to foot the bill to transport their Roma populations, forcibly if needbe.
The next question is 'where'. I could see educated Romanies making an Indian play on the basis of their attested ancestry. While the British likely wouldn't be keen on the idea, they'd be functionally unable to stop a Romany migration funded by other states in Europe looking gleefuly to solve their 'gypsy problems'. India is massive, the Suez Canal will revolutionise transportation, and British government in many areas of the subcontinent is slack.
By 1900, a small, but significant population of Romanies would have already made the journey. They would remain a highly distinctive population wherever they settled, laying the foundations for future additions. Whether they could fit in with the indigenous population is open to debate - in all likelihood, they would encounter antagonism from castes holding similar artisan roles. However, given their nomadic traditions, it's unlikely they would remain in one, concentrated area.
Moreover, emigration to India would remain a niche interest, and most Romanies would continue to live in Europe. Interest in India would only really take off if persecution began on a Nazi-like scale in Europe, at which point India might seem like a more attractive option. Then - and only then - might you start seeing the numbers leaving necessary to build a real, albeit non-sovereign, 'Romany Nation' in India.