The key event in the creation of the Manhattan Project and hence the atomic bomb wasn't, contrary to popular opinion the Einstein-Szillard memo to FDR, which was written in 1939.
The letter resulted in the S-1 Uranium Committee, which basically did very little and had a tiny budget. This was partly due to the fact that their understanding was that tons of Uranium 235 would be required, and hence the project was not very practical.
In 1940, the British (in fact Otto Frisch and Rudolf Peierls working for the British) correctly appreciated that the amount of Uranium 235 required was far less than previously thought (pounds rather than tons).
In late 1940, the British MAUD committee produced a report outlining the feasibility of the bomb, which was sent to the Americans but ignored. The British started their "Tube Alloys" project but couldn't afford to prioritise it as they were fighting for their lives.
The key event was the visit of Mark Oliphant of the MAUD committee to the USA in 1941, where he impressed on the US scientists the feasibility and urgency of manufacturing the bomb. After these meetings, in December 1941 Vannevar Bush created the Office of Scientific Research and Development, after that the Manhattan Project took off and quickly eclipsed the British project, which was eventually (1943) folded into it.
So, there's a simple way to delay the Manhattan Project: Oliphant's plane crashes. The S1 committee then carries on doing nothing much and the MAUD report carries on being ignored.
Eventually, the British send another envoy or the US put two and two together on their own and the project kicks into gear. Six months to a year delay, easy.
References:
http://en.wikipedia.org/wiki/Einstein-Szilárd_letter
http://en.wikipedia.org/wiki/S-1_Uranium_Committee
http://en.wikipedia.org/wiki/Frisch-Peierls_memorandum
http://en.wikipedia.org/wiki/MAUD_Committee
http://en.wikipedia.org/wiki/Tube_Alloys