My Eevee, Kit, had hiccups really bad a few days ago. If you can get him to hold still I found asking him to drink fro the wrong side of the bowl helps.

Like this.

[He digs around in his bag, and holds up his water bowl, tilting it slightly- if it wasn't empty it's be leaking.]

See if you can get him to try and drink from the far end. The effort of having to focus on your breathing and drink at the same time helps reset the diaphragm. Water WILL get everywhere though.