I see this thread is about 1.5 years old now, but I guess it might help others...
Could you tell us the IP address and netmask of one other device (should not matter which one) in your current network?
That would make it possible to calculate the range of valid IP addresses for your network, instead of relying on blind guesswork.
If the netmask is 255.255.255.0 (as is common on home networks), then the first 3 parts of the new IP address must be same as on all the other devices, and the last part must be chosen to be unique. The last part has some other restrictions too: .255 is always reserved for the broadcast address, and .0 for "network address": they should not be used for regular devices. Your default gateway (= cable modem or whatever, your gateway to the Internet) is probably either .1 or .254 (either the lowest or the highest available regular IP address).
If you don't have assigned static IPs on any other device in your current network, then one of the devices probably works as a DHCP server. Cable modems and other Internet gateway devices intended for home use often do this by default. In that case, setting the printer to use DHCP and then relying on Bonjour to find the printer might be the easiest solution, but has the disadvantage that the printer may sometimes get a different IP address depending on which order the devices in your network are powered up. The DHCP server is supposed to maintain a table of previously-seen devices to minimize this problem (= always assign the same IP address to a device it has seen before, if possible), but on cable modems and similar devices, such a table might be cleared when the device is powered down.
Your Airport Extreme base station *can* act as a DHCP server, but if it's acting as a wireless signal repeater, it probably *should not* - so it probably has its DHCP server function disabled.
(A single IP network segment can have multiple DHCP servers only if they are configured to work together. Such a configuration is "enterprise-grade networking", and outside the scope of most home set-ups.)
Another possibility might be to configure your DHCP server to always assign a particular IP address to your printer, if the DHCP supports that feature. For that, you'll need access to the DHCP server configuration, and the Ethernet address (also known as MAC address) of the printer. That is a string of 12 numbers and/or letters A-F, possibly delimited by columns or dashes. It might be printed to a sticker on the Jetdirect card, and it should be visible in the Jetdirect configuration print-out that you can get from the printer itself.
The third possibility is to just assign a suitable, non-conflicting static IP address to the printer itself. The DHCP *should* automatically detect that the IP address is occupied and avoid trying to assign it to any other device; however, in practice this does not always happen.
Often, even a very simple DHCP server can be configured to restrict itself to just a sub-set of IP addresses; you could then use the addresses *outside* this subset as static IPs for printers and other devices that might benefit from a static IP. For example, if your network has netmask 255.255.255.0, uses IP addresses like 10.1.1.x, that means the total address space of your network is 10.1.1.0 ... 10.1.1.255. Now, as I said before, .0 and .255 are reserved for special purposes, so only 10.1.1.1 ... 10.1.1.254 are usable.
If your gateway device is 10.1.1.1, then you could let the DHCP server assign addresses 10.1.1.2 ... 10.1.1.199, and leave the addresses 10.1.1.200 ... 10.1.1.254 available for statically configured devices, like your printer.