Hi -- I feel ya with the screaming kids, I have 2 screaming kids of my own. Sounds like all you'll need is an original R4 with 2GB microSD. It'll work fine in your DS (from Australia) as they're all region free.

This is the best deal IMO - Original R4 with 2gb microSD for $12.99 w/free shipping:
http://www.ishopvideogame.com/r4-ds-2gb-kingston-memory-card-p-1595-58.h...
(note: R4 vendors no longer include the software needed to run R4s, but you can download the needed firmware for this R4 model here: http://www.wiilovemario.com/download/R4DS/kernel/R4-v1.18-English-Kernel...)

If you plan on getting them one of the newer DSi models then the R4i SDHC with 2GB (or bigger, up to 32GB) microSDHC will work. This model will work with all the Nintendo DS, DS Lite and DSi handhelds. This one is $29.99 w/free shipping:
http://www.ishopvideogame.com/r4i-sdhc-2gb-sandisk-memory-card-p-1643-58...
(note: Same with this one.. R4 vendors no longer include the software needed to run R4s, but you can download the needed firmware for this R4 model here: http://www.wiilovemario.com/download/R4DS/kernel/Red-R4i_English_V1.14b....)

Hope that helps with the screaming kids! :)