The _gaq.push method fires GA Events directly from the carousel. When you convert to GTM, you fire these events indirectly using GTM.
The first step is to convert the _gaq.push calls to fire custom GTM events using dataLayer.push(). In addition to firing the GTM Event, you'll have to push some sort of carousel item identifier into the dataLayer. Usually this is the URL of the image or a caption. Likely the _gaq.push call was also sending this identifier.
Once you have this working, create a rule that looks for that GTM event, and then create a GA Event tag that fires when the rule is true. You'll also want to create a GTM macro that pulls the identifier from the dataLayer. Use the macro in your GA Event tag to pass the identifier to GA.
See the Using the Data Layer with HTML Event Handlers section of this page https://developers.google.com/tag-manager/devguide for information on firing custom GTM events.