My wife used to be a librarian so I know a thing or two - I don't imagine there's a lot of room in the budget. But I still think you should stand your ground.
Do some research on the units. Find out how many amps the old window shakers use when running - read the label - and compare that to the new 8,000btu units. I bet the new ones are close. If it's the same or less, the higher output models are an easy call, providing better comfort for the same running cost. If it's lower, just point out that the newer models cost a bit more today but cost less to own, ultimately saving the library money while providing a more user friendly environment.
Really, two 8,000s probably won't be enough during the day, but they'll catch up overnight I think. Anything you can do to improve the insulation or otherwise reduce the heat load on the building will help (if you have a flat roof, paint it white with Kool Seal or similar). That's another cost but what it saves in AC will pay for itself in one year.
If they won't pop for both, ask them to spring for one this year and the second one next year. That spreads the cost out but by placing the larger unit in the reading room, you improve conditions for users first and start enjoying the energy savings immediately. Anything else you can do, like improving the lighting with lower-consumption lamps, timers, etc can probably be justified with simple math. For instance, I relamped with lower wattage but similar output lamps that cost about 4x as much as the originals...but over their life, each lamp saves about $12 in electricity. That was an easy no-brainer and by the time I had relamped the entire facility, our electrical bill was down by about $3000 per month. If you can get the bosses to see how the math works out, they will LEAP onto your bandwagon.
Good luck with it.