To be slightly pedantic, in the hypothetical situation cited, the SB will be issued by the engine manufacturer and and the SB will be approved data, while the AMM isn't. For engines the engine manual carries more weight than the AMM every time.
For the more realistic situation of a confict between an airframe SB and the AMM we must first qualify the conditions I discuss - Boeing aircraft, Boeing SB.
Notwithstanding matkat's belief that the AMM is an approved document, Boeing have many times advised that since the AMM is not approved by the FAA, the AMM and IPC are "provided for the information and advice of maintenance personnel only and certifications can only be made to the approved drawings, which are the only FAA approved documents" Overestimating the status of the AMM and IPC has led many an LAE astray, I'm afraid. Although the AMM is based upon the approved drawings, the latest manfacturer's drawing approved by their regulatory body will always overrule the AMM or IPC. Boeing (or other manufacturer's) SBs will generally be drafted on the basis of new drawings, therefore it is most likely that an SB will supersede the AMM. The proper response to a conflict is therefore, to release the aircraft to the most restrictive of the possible outcomes while the conflict is referred back to the manufacturer, quoting chapter and verse. In most cases you will find the SB wins. and the manufacturer advises that an AMM revision will be issued shortly. Such matters are the bread and butter of Technical Services or Development Engineers, so I'm surprised no-one seems to have considered consulting them.