Sapphire. If you don't have this, and the setup for this, then you're not even ready yet for friends to come over.
I thought I stated in my OP that I do not have a CD drive.
Regardless, my friend came over and first we watched Dead Pool on BluRay. Awesome movie btw. Then we played Bomberman '93 Special (multiplayer only) for an hour or so, and Bonk III after that. Great matches overall though I think we both had more self kills than proper victories. In hindsight I should have suggested Parasol Stars as our second game since Bonk III got tiring going into the second stage. There are a lot of vertical areas which can be a pain to back track if one player falls down off screen. We did reach the Stage 2 boss before squandering our remaining lives. Overall not perfect multiplayer and probably better experience played solo. I own Bonk and Bonk II CIC but haven't really played Bonk III much on my Everdrive. After that ordeal my friend decided he had enough of Turbografx so we played a few online Mario Kart 8 wifi matches and a bit of Mario 3D World on my Wii-U before it was time for him to leave. Thank you all for the suggestions though. Next time he comes over we'll definitely be revisiting the Bomberman series games, and I'll try to sneak in a bit of Parasol Stars.
I wish my fiance enjoyed games half as much as I do, then I'd at least get to experience local multiplayer more often...
Have I suggested Hit the Ice and TV Sports Hockey?
Final Match Tennis on PCE may be the best 16-Bit version of pong ever.
I may give the sports titles a try sometime. I'll need to see how they play first in single player though. My friend wanted to play NFL Blitz again but alas my translucent smokey N64 is dismantled in preparation for an upcoming LED mod.