Since 1948:
My guesses would be:
1948:Truman
1952:Ike
1956:Ike
1960:Nixon
1964:LBJ
1968:Nixon
1972:Nixon
1976:Ford
1980:Carter
1984:Mondale
1988:Bush Sr.
1992:Bush Sr.
1996:Clinton
2000:Gore
2004:Kerry
2008:Obama
Here's my reasoning:
1948: Truman's Administration proposed the Marshall Plan and helped Western Europe rebuild. Thus, he would win Western Europe.
1952: Ike was the liberator of Western Europe from Nazi oppression. Also, he was perceived as more experienced on military and security matters. Thus Ike wins.
1956: Ike wins for the same reasons as in 1952.
1960: Nixon wins since he portrays himself as more experienced than JFK and since he is perceived to have better knowledge of the inner workings of the govt. (since he was VP). Since Western Europeans are happy with Ike, and Nixon promises to continue Ike's policies, Western Europe votes for Nixon.
1964: Since Western Europeans are afraid Goldwater is too hawkish and might start a nuclear war, most of them vote for LBJ.
1968: Nixon promises to end the Vietnam War, and since the Democrats started that war, Western Europe trusts Nixon more.
1972: Nixon withdraws most U.S. troops from Vietnam and portrays McGovern as a weak leader who would be unable to confront the U.S.S.R. and stop Soviet aggression. Thus, he wins Western Europe again.
1976: Ford had good relations with the U.S.S.R. and was perceived as more experienced. Thus, he wins.
1980: Reagan is portrayed as too extreme and as someone who might start a nuclear war. Thus, Carter wins.
1984: Reagan isn't as extreme as thought, but his refusal to negotiate with the U.S.S.R. (and thus continually poor relations with the Soviets) upsets many Europeans. Thus, Mondale wins.
1988: Reagan establishes good relations with the U.S.S.R. and pursues detente. Thus, his VP, Bush Sr., wins.
1992: Tough one. The Cold War just ended, but many Europeans are happy with Bush Sr.'s job performance. Thus, Western Europe votes for Bush Sr. again.
1996: Clinton has good relations with Western Europe and Russia, and Dole is portrayed as a reckless unilateralist. Thus, Clinton wins.
2000: The GOP is portrayed as reckless unilateralists once again. Thus Gore wins.
2004: Same as 2000. Thus Kerry wins.
2008: Same as 2000. Thus Obama wins.