OK, based on the rules submitted to the RI Secretary of State, this is my best guess on how Rhode Island’s Republican delegates will be allocated.
1. All candidates who received more than 15% of the vote are eligible to receive delegates. For the 2012 Republican primary, that means Mitt Romney (63.0% of the vote, with 14 of 135 precincts left to report with all precincts in) and Ron Paul (23.8%).
2. 8 delegates are awarded from each Congressional district (that part I’m pretty sure of) based the proportion of the statewide vote going to candidates who broke the 15% threshold (that part I’m less sure of, see update II below). At the moment, that means Mitt Romney would receive 5.8 delegates per district and Ron Paul would receive 2.2 delegates per district. Assuming traditional rounding is used, that’s 6 for Romney and 2 for Paul.
That means, with 121 of 135 precincts reporting, and under the assumptions that the statewide total is applied to each Congressional district and results are rounded to the nearest integer, the unofficial leaders are:
District 1, Leading Romney Delegates:

John F. Robitaille 3793
Lynda Adams-Robitaille 3152
Daniel Patrick Reilly 2955
Robert J. Gallagher 2339
Amy Lynn Gallagher 2146
Barbara Ann Fenton 1903

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Mark Smiley 1874
Peter D. Costa, JR. 1861
Giovanni D. Cicione 1844
Tara L. Pinsky 1746
Steven E. Santos 1455
Joseph H. Lorenz 1444

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Rudd C. Hall 1169

District 1, Leading Paul Delegates:

Richard E. Ford 1103
Daniel S. Harrop 1080

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Douglas P. Berge 1075
Robert A. Marquis 1063

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Paul Andrew Schmidt 1058

District 2, Leading Romney Delegates:

Allan W. Fung 4052
Donald L. Carcieri 4019
Suzanne O. Carcieri 3705
Scott Avedisian 3357
Ruth A. Zaccaria 2620
Doreen Marie Costa 2455

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William K. White 1617
Richard A. Mumford 1566
Scott Bill Hirst 1539
Eileen G. Grossman 1499
Elizabeth O. Smith 1464
Clifford M. Carlson 1077

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Diane S. Nobles 1070

District 2, Leading Paul Delegates:

Andrew J. McNulty 1120
David J. Aiello 1062

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Erik E. Turgeon 1028
Rachael L. McIntosh 981

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Justin K. Price 975

UPDATE:
CBS News lists last night’s result as 13 delegates for Romney versus 3 for Paul, in their estimated delegate count chart.
UPDATE II:
The delegate selection rules summary on the State Republican Party website says that…

Each presidential candidate who qualifies for delegates and alternates shall receive a proportional share of the delegates and alternates in each CD based upon the percentage of the vote in that CD,

…so using the town-by-town totals on the Board of Elections website, I calculated what the delegate allocation would be in each Congressional District if they were treated separately. Again, using traditional to the nearest-integer rounding on the proportion of votes received by the two 15% qualifiers, Romney gets six delegates in both districts and Paul gets two — though in the Second District the split came close to being 5/3. If fractional (and not just factional) delegates were allowed, the resulting split would be 5.6/2.4.
It is also worth noting that Burrillville voted in the First District primary last night even though they will be part of the Second District going forward. Was this a mistake? It makes objective sense for a primary election to be carried out according to the rules that its corresponding general will use, but the legislation that realigned the districts is ambiguous on the subject, first saying that it takes effect immediately, but also containing a long section explaining how immediately means after September 2012. Given that one Ron Paul delegate race last night was decided by a margin of 5 votes, whom Burrillville voted with may have had an impact on the final result.