The best alternatives to Gfycat are Sendspark, Coub, and Netflix GIFs. If these 3 options don't work for you, we've listed a few more alternatives below.
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Sendspark is a web-based platform for businesses to build personal connections with their customers - with video! We believe that the future of business communication should be fun, personal, and engaging.
Coub is a video sharing website available on both iOS and Android. It allows users to create and share looping videos up to ten seconds long, using existing video from YouTube, Vimeo, or their own files.
Chrome extension to create GIFs from Netflix content! Just go to Netflix, press "g" to share your screen, and the GIF will auto download (after 30 sec or so).