There is no "option" for this in the content carousel plugin, as it uses CSS transitions. You can however override the CSS transition by doing the following:
Add a custom class to the carousel container, for example class="mycarousel":
<div data-carousel data-carousel-items=3 data-carousel-loop=true data-carousel-dots=true data-carousel-autoplay=3000 data-carousel-responsive=true data-carousel-shuffle=false class="mycarousel">
Add the following to Settings > Custom > Custom CSS:
.mycarousel .owl-stage {
transition: all 2s !important;
}
In the above, duration is set to two seconds. You can change it to whatever you like, including decimals, for example 2.5s or 0.2s.