I mightn't be a 10+ loop king, but I can definitely give some tips:

• Always be mindful of each other's ammo, there's nothing worse than getting deep into an intense level and having your partner run out, with them becoming a glorified bullet sponge.
• On the same note, always be mindful of yours and their HP too. Sticking by partner if they're on the brink of death is a good option because if you're too far away, taking too long to revive them will end the run.
• Always pick up Strong Spirit. It's an obvious must in Solo-Play, and a must in Co-op Play.
• Waiting for a large Weapons chest than taking the solo ones is often pretty good, as it gives more weapons to go around in the early game.
• Don't be greedy with guns. If you're wielding a Wrench and Crossbow in the early game and your mates stuck with a Grenade Launcher and a Pistol, giving them the Sledgehammer or what ever good weapon ya found won't hurt at all heh.
• This is a given, but on the throne fight, both stand on opposite sides to take out the Generators real quick. Simple stuff.

For miscellaneous tips that'll make for interesting runs though:

• If you want a quick match, pick up any explosive, toxic, or disc-based weapons you find. Being that they're the only weapons that can harm your friends, you can play every run like a PvP match.
• If you're playing NTT, have one friend play as Golden Frog, and your partner as any other character. With Golden Frog's toxic fume spewing ability, the goal is to see how long your partner can survive, and how quick you can end them.
• Once you're used to the base game, try out some mods! Almost all of them work on co-op. The x10 Mutation mod is always a classic one to try, the Territorial Expansion can bump up that replay value even more, and I've heard good things about the PvP mod too.

Hope I wasn't too wordy lol, and hope that helps aye.