You can get NiMHs that have 2+ amp-hours off the shelf at the grocery store (got two 2000mAh rayovacs in my hand right now in fact.) Decide how many days worth of runtime you want, and double them up in parrallel until you've got enough. You'll be best off to only run them down a small bit except during emergencies (like a large number of cloudy days) e.g. it'll take 9 NiMH's in series to get 12V (1.36V nominal per cell, mine run 1.44 fully charged) though likely you'd use 10 in a device that ran off alkalines since they can take the extra voltage. If they were 2000mAh that would be a 10 hour runtime for the transmitter, deep cycle, or 2 or 3 hours if you want to baby the batteries to extend life. Add 9 more in parallel then that's 20 hours deep cycle, etc.
If you don't mind changing the batteries, something a little cheaper than the charger linked below would work well (note the price includes 10 NiMH cells.) Otherwise you'll either want separate 9V and 12V charge controllers and panels, or a DC-DC stepdown with the below 12V system or equivalent. Unfortunately whenever anything remotely "hobbyist" gets involved prices skyrocket. NiMh's AA's cost about $2 per cell, and a 5-10W panel should do it -- it's just the stuff to jam in-between that might cost a bit -- to wit, a Nimh 4-cell wall wart charger is like $15, but as soon as you try to get one to run off a panel that wasn't built in to start, you're paying out the nose for no good reason.
This would work dandily as a one-piece solution for the transmitter:
http://www.cetsolar.com/deltacharger.htmThere's some other stuff on this page worth looking into -- lower wattage, but very affordable. No vendor endorsement implied -- do shop around. BE CAREFUL! There are gougers in them thar hills.
http://www.cetsolar.com/solarbatchargers.htm