Asked if 10-month-old Ryan would see a united Ireland in his lifetime, Mr Adams grinned: "Of course. Maybe even his granny will." At which the old lady standing next to him growled: "I'm not his granny. I'm his great- granny." Perhaps "the Shinners" have something to learn about the politics of the doorstep.
In the main street of Carrickmore, Tyrone, in the heart of what the tabloids call IRA bandit country, the Sinn Fein president is on the stump on home ground, trying to persuade voters to elect his party to the 110-seat Northern Ireland peace forum on Thursday. The forum's task will be to act as a confidence-building "gateway" to all-party talks on an overall settlement for the province.
A hundred yards away from Mr Adams and his photo opportunity was a reminder of how difficult it will be to find such a settlement: a well-tended republican garden of remembrance to more than 50 dead "patriots". The Irish tricolour flies from lamp-posts, decorated also with fading "Brits Out" posters. Outside the village is a roadside memorial to three Provo "volunteers" ambushed by the SAS.
Gerry Adams on the campaign trail is even now rather a novelty. He cancelled a local launch of his party's manifesto for Thursday's election in favour of a brief walkabout followed by a private strategy lunch at the Old Charm Inn. At least, that's what it looked like. The presence of several square-jawed gentlemen discouraged nosiness. An hour later, the new charmer emerged to tell the Independent on Sunday: "We are contesting the election. Whatever mandate we get should be respected. Mr Major can hardly pontificate about the primacy of the ballot box if he refuses to recognise the rights of those who vote for our party."
Sinn Fein has decided to stand although it will be excluded from the talks themselves until the IRA announces another ceasefire. As to the prospects of a cessation of violence, Sinn Fein remains coy. West Tyrone candidate Pat Watters insists: "We don't know what is going to happen." He is scathing about the SDLP, arguing that it can be bought over. "We can't. We stick to our guns," and then, recognising his faux pas, "so to speak". Others found grim humour in a reporter's question: what was the Army presence here during the Troubles? "Whose Ormy?" shot back a Sinn Feiner.
Otherwise, the entertainment is at the expense of Sammy Wilson, press officer to the Rev Ian Paisley's puritanical Democratic Unionist Party. Photographs of Mr Wilson, a high-school teacher, gambolling naked in a meadow with his girlfriend in full-frontal nudity were published in last week's Sunday World. Mr Paisley condemned a "vile conspiracy and debased press standards", but offered that his public relations man would be finally accountable to his Maker.
Everyone agrees this single-issue election is peculiar. It has been called at the insistence of the Unionists to choose the 110-member forum. The electoral system for the poll is a mixture of the current Northern Irish system of Single Transferable Vote and a list system, on which there are some 31 parties. This will give smaller parties, such as Sinn Fein and the DUP, more chance of significant representation, and is designed to prevent domination by the two main unionist and nationalist parties, the Ulster Unionists and Social Democratic and Labour Party.
The electors can only vote for a party of their choice. Television advertising is confined to a government exhortation to vote: "Your Choice, Your Voice, Your Future" against a backdrop of children.
Essentially it is a struggle for popular mandate. There are two battles going on, separate but interlocking: one for the soul of Irish nationalism, the other for the soul of Ulster unionism. Sinn Fein versus John Hume's constitutionalist SDLP, Mr Paisley's hard-line DUP versus the traditionalist Ulster Unionists led by David Trimble. Tribal loyalties suggest that the outcome is already known, but there could be dangerous upsets at the fringes. Some detect a polarisation of voting intentions that would make peace negotiations even more difficult.
All the party leaders were among West Tyrone's "dreary steeples" last week to drum up support in this, a new constituency that will send an MP to Westminster for the first time at the general election. Joe Byrne, a business studies lecturer in the county town of Omagh, widely tipped as the SDLP candidate for parliament, was busy peacemongering even in the Sinn Fein enclaves of Strabane, arguing: "We have to build a viable, long-term settlement in Ireland. This is a time when real discussions could lead to something. Our people have had a taste of peace, and they want it to be maintained." Peace has often been in short supply hereabouts.
Francie Mackey, a psychiatric nurse and one of Sinn Fein's candidates for the five West Tyrone seats on the forum, claims his party could win two. "People who used to stay at home are now turning out to vote Sinn Fein. They recognise that the election was unnecessary - we should have gone straight into all-party talks - but they recognise we have to protect our mandate."
Sinn Fein is now the largest party on Omagh District Council. It is not easy. Mackey himself, aged 42, married with three children, has survived three attempts on his life. Last week, a coroner's court in Omagh heard that the Loyalist murderers of an SF election worker in Castlederg are known to the police, but there is insufficient evidence to charge them.
On the other side of the divide, the unionist community in Castlederg (pop 4,500) has suffered 23 murders and more than 70 bombs. DUP candidate Thomas Kerrigan, 57, a sales representative who lives in the village, insists: "This is the heartland of Loyalism. It has suffered a lot over 25 years of terrorism. But we will be recognised as the traditional unionists who are taking a stronger stance against the republican element."
His Ulster Unionist rival, teacher Derek Hussey, another Castlederg man, is equally adamant that "we shall not shirk from our duty of challenging the pan-nationalist front head-on."
Best estimates suggest that the SDLP will take two of the West Tyrone forum seats, Sinn Fein, the DUP and the Ulster Unionists one each. Overall, the Ulster Unionists are likely to retain their prime place with around 30 of the 90 elected seats, with the SDLP second with about 22. Mr Paisley's DUP should take at least 15 and Sinn Fein as many as 10. But the election is only the beginning, and it may not even be that if there is no IRA ceasefire. Perhaps, as the fundamentalist road sign on the Belfast road out of Tyrone suggests: "Hell Hath No Exits."