Real creativity is needed here. I'm in Belfast currently, and the international flight options are certainly limited. Dublin has more options, and as a result, some lower prices. Bus and train service from Dublin to Belfast will be quite adequate so an internet search for options and prices will help. My sisters took the train from central Dublin to central Belfast last November, and the trip took around two hours so if the prices justify flying through Dublin, there isn't a huge extra time investment.

Your travel dates are part of the problem. August is one of the peak travel times in Europe; as a result, prices jump accordingly. I am assuming the dates for travel are inflexible, but if they could change, you might find some cheaper fares, especially by late September/early October. Since you mentioned the travelers are students, I think my assumption about the travel dates is probably correct so that won't help much here.

The front end will also create a problem. As you might imagine, Spokane is not a major flight center, and I'm sure there's little market pressure on prices. Another starting point, like SEA, would increase the chances of finding a lower fare, but I know that Spokane is roughly 300 miles from Seattle so that it's not easy to just drive there.

But I see you have Southwest, American, and Alaska flying in and out so there is the potential to use points in a limited fashion to get to an international hub, like Seattle or San Francisco or Los Angeles. If there is an option to open a credit card that earns points, either a Southwest card or a Chase British Airways card might be worthwhile. If interested, you should check out FT's airline and credit card forums (or have the students do it--make 'em work a bit!) for details on how these programs work, but in very TL, DR fashion, Southwest points are revenue based so that each point is worth some value on a published fare while BA has a distance and segment based program that makes it possible to do a roundtrip on AA or Alaska for 9K--so long as the nonstop distance is less than 650 miles. I believe each card has a 50K signup bonus currently, which might, might be enough three travelers.

Finally, it's possible that routing through an airport that wouldn't immediately come to mind could also save money. For instance, AMS seems to attract some low fares. Two Norwegian airlines, Norwegian and WOW Air, are trying to put some downward pressure on airfares but mostly to the East Coast. Why could this even possibly help? Ryanair in Dublin is famous for really low fares from lots of European airports to Dublin--and some really outrageous fees if a traveler isn't careful about booking or baggage or other items Ryanair charges for that wouldn't have occurred to a traveler 20 years ago. With this in mind, however, a trip through another European gateway that Ryanair services might help to lower the cost.

So, if the fares are to come down significantly, some form of the following is probably going to necessary: drive to Seattle/use a credit cards' points to get to SEA, SFO, LAX, DEN, ORD to get to DUB or to get to AMS, OSL, or some other European gateway to DUB, train/bus from DUB to Belfast. Would you or I like to travel that way? No, but these are young students who may be willing to take on some adventures to save a significant amount of cash. As mentioned above, have them do some of the heavy research here on FT and through Google Flights and other similar services to try to piece together the puzzle.

But, if they're unwilling to do the research/odd travel, and the question is going to remain, what's the cheapest they can get from Spokane to Belfast for specific travel dates this August, you've probably already got the answer.