More info, please ... otherwise the only valid reply is "it depends"
* max print size (letter vs 13x19" vs wider)
* expectations of photo print quality, as applicable
* suitability for re-filling, as applicable
* quantify of printing ... infrequent vs often vs heavy use
I'm aware of Canon Selphy printers, which may meet the height requirement you mention. My impression is that they are very slow, meant for infrequent use, and the cost per print is high.
According to the Canon spec page,
Canon U.S.A. : Consumer & Home Office : SELPHY CP800 Black
the cp800 is 2.5" tall.