There really isn't any such thing as 240p video. All old gaming consoles sold in North America (and Japan) output NTSC video, the only format North American TVs accepted at the time. This is actually a 525 line interlaced format, of which 485 or more lines are visible. The standard way of encoding NTSC video digitally only uses 480 lines, thus it's commonly called 480i, but really in its analogue format it's 525i and that's what these old consoles all output.
What people call 240p video is actually just NTSC video where the two interlaced fields are identical (or alternatively where one field is blank). Unfortunately, for whatever reason a lot of modern electronics has problems with this. My AV receiver has no problem with what it detects as 240p video, at least not with anything I own, on the other hand my TV can't seem to handle it through its component inputs, though it works fine through its composite inputs. I suspect the problem is largely due to software bugs, the hardware has no problem with it, but the firmware refuses to support what it mistakenly thinks is a non-standard resolution.
Anyways, the upshot of all this that potentially any AV receiver that can convert 480i analogue video to HDMI could work with your old consoles. A guy I know has his NES connected to his Denon receiver in order to play games on projector. My Yamaha receiver (HTR-8063) works fine with the "240p" video my original PlayStation outputs. If you do end up getting an AV receiver for this then just make sure you can easily return it if it doesn't happen to work with your consoles.
Personally, I think the ultimate AV receiver for retro gaming is the Yahama RX-A1010. It's got ton of inputs, including S-Video, and shouldn't have any problems with "240p" video. The problem is that it's far from cheap. A cheaper receiver can potentially do the job, but you lose S-Video which is a big jump up in quality over composite for those consoles that support it. If you've got a lot of old consoles then you'll be less likely to be able to hook them up all once, and so you'll need external switch boxes or have to hook them up manually.
I think 2012 Yamaha models are step down over the 2011 models for retro gaming. Most of the 2011 models supported analogue-to-analogue conversion and analogue on-screen display, which is nice if like me you like to play classic games on a CRT TV. Of the 2012 models only the RX-A2020 and RX-3020 support this.