Another puzzling aspect of this question is that there don't appear to be loads of complaints all over the web from people unable to install amazon payments because of this problem.
If I may make an off-the-wall suggestion ... are you actually sure that it needs curl version 7.26 or later? I had a look at
and yes it does indeed say,
"Note: Be sure you are using PHP version 5.2.6 or later and curl version 7.26 or later when using the PHP code samples listed here."
But ...... could it be that this statement is only there because the person putting this code together tested it with those versions of curl and PHP, so, to be on the safe side, they said that these versions are required?
By the way, I had a look at some of the PHP samples on that page, and they call
$responseBody = curl_exec($curlHandle);
instead of something simpler like
system ('curl ...');
so it would indeed be necessary to pursue part 2 of sXi's suggestions instead of part 1.