Can I use a PC74HC161P as a switch to either ground one board or another? If so, how would i wire it? Switch one on and the other off when there is a reset.
Not by itself, no. You'll need some other part to convert the output from the counter into something that only enables one ROM or another.
You can use multiplexer/demultiplexer for that. You should be able to wire both roms on one address bus, and use 8-16 bit multiplexer to choose data bus.
I have some 74LS139. Could they be used to make a switch or in combination?
Sure, in combination.
Details depend on exact details of what you're trying to do (e.g. one PCB with multiple ROMs, multiple preexisting PCBs, &c)
I wanted to wire 2 gameboy games to a super gameboy board and use the ground to select which one plays or that what I thought would work.
Use the 74'139 as:
1- from the SGB, connect A15 ("/LOSEL") and /CS ("/HISEL") to the two half '139's /E inputs
2- from the counter, connect QA (the least significant bit output) to the two half '139's A inputs
3- from the '139, connect the /Y0 outputs to A15 and /CS on one cart, and the /Y1 outputs to the other cart
Configure the 74'161 to count up by one whenever the /RESET signal goes low
Thanks lidnariq!