I would measure the gross outside dimensions of it. My Amati, for example would fit into about a 32"x14" rectangle. Then look for a euphonium gig bag that provides that space. These horn's aren't big, the bells are typically small compared to contemporary euphoniums, and they don't extend much (if any) horizontally outside the "footprint" of the oval body. But they are longer than the average euph (mine appears to be about 6" longer, overall, than my Mack Brass euph). So a standard euph bag won't work.
A small tuba bag would work. For example, the Gard 61-MSK. A Wagner Tuba bag would probably work (Marcus Bona has one: $$$...$$$ ). And a small F tuba bag would work. But you're probably looking at higher cost than you want to. Alternatively, find some reasonably priced duffel bag that it would fit in -- either padded, or that you could add padding to.
Gary Merrill
Wessex EEb Bass tuba (DW 3XL or 2XL)
Mack Brass Compensating Euph (DE N106, Euph J, J9 euph)
Amati Oval Euph (DE 104, Euph J, J6 euph)
1924 Buescher 3-valve Eb tuba (with std US receiver), Kelly 25
Schiller American Heritage 7B clone bass trombone (DE LB K/K10/112/14 Lexan, Brass Ark MV50R)
1947 Olds "Standard" trombone (Olds #3)