Without giving away precisely what I'm planning to enter into
this contest, here's a few things I noticed while sketching out the possibilities:
1: The RIOT includes a timer, but it's a bit awkward to use if you happen to want to accurately time intervals longer than some fraction of a second, as it has no convenient free-running mode. You can apply several divisors to the Phi2 clock input, but these divisors are reset as soon as the timer expires, and the timer itself has only an 8-bit counter which makes it considerably less capable than the VIA.
2: The 6507 is not directly available in a CMOS equivalent. However, most of its pins correspond closely in layout with those of a full 6502. Enterprising hobbyists could easily make a PCB layout that can accept either the 28-pin 6507
or a modern 40-pin 65C02, in overlapping mutually-exclusive positions and with equivalent capabilities. Useful if you want to reduce power consumption, or you don't have a real 6507 to hand. Don't forget to tie the unused inputs of the 65C02 socket off appropriately: BE, /SO, /IRQ and /NMI.
2a: The RIOT is also not available in a CMOS version, but its pinout is nowhere near that of the VIA, so it's more complicated to do a similar substitution trick with that. In any case, the VIA requires different software to use. It's a relatively simple device, so perhaps a discrete-logic equivalent can be built if an extension of battery life is desirable.
3: By wiring the A6 line of the RIOT to A8 of the CPU and /RS of the RIOT to A9 of the CPU, you can have 64 bytes of RAM in each of the zero-page and stack areas, with the I/O moved safely into the $02xx range. Both RAM segments will be mirrored four times in each CPU page. If the RIOT and the ROM are the only devices in the system, then inverting A12 should give you suitable /CE for the ROM, while raw A12 gives /CS2 for the RIOT. Obviously you'll need to do something more sophisticated if you put another device in the memory map as well.
4: The AM2716 is a 24-pin UV-erasable EPROM. However, it will fit in a 28-pin socket to fit a modern 8Kx8 EEPROM, as long as socket pins 23 (Vpp on the 2716, A11 on an 8Kx8) and 26 (Vcc on the 2716, NC on an 8Kx8) are both tied directly to +5V. The four "dangling" pins of the socket also need to be tied off sensibly, so that you can actually use an 8Kx8 device in it - much more convenient to program and erase, and also consuming less power when in use. Because A11 is tied high, a 2KB ROM image won't be seen at the start of the larger ROM, but must be written further up, at either $0800 or $1800 depending on which way you tie A12 on the socket.
In general, the specified parts - being ancient NMOS technology - have relatively high power consumption, so are not well suited to a battery-powered project. But I think something reasonably pretty and/or useful can still be done with them.