Disclaimer… this is a low budget setup pieced together and is kept in the garage for patio and garage speakers. Quick backstory, bought a cheap used "HT in a box" receiver online that only came with the subwoofer. Actually sounded pretty good for what it was. Receiver gave up the ghost recently so I found an Onkyo for cheap locally. Here's the issue…

Subwoofer is a passive speaker with separate red/black connectors like all of the other speakers. The "new" receiver only has the RCA "subwoofer out" connection. One suggestion I was given was to just connect it to the center channel terminals. It sounds ok, but playing with the crossover, it's hard to find a balance of not too much distorted bass coming from the patio 6" speakers and too much mid/treble being sent to the subwoofer.

Any ideas? One thing I was thinking was cutting one connector off of an old subwoofer cable I have and splitting the wire to the sub. Wondering if the "sub out" is also amplified. Doesn't say "pre"…

Sub outs are not amplified. Sounds like you need an amp or really just a halfway decent powered subwoofer. If you want to keep it find a cheap class D amp with enough power for it. Don't connect it to one of the other channel outputs as your receiver likely lacks the ability to limit the frequencies sent to only that channel. That's what the sub out is for...except those aren't amplified.

If the sub has ins and outs, run the wires to the sub and then to the speakers.
Otherwise, get a cheap crappy mono amp like this:
amazon $30

Connecting to the center will not work. The sub needs to get all of the low frequency sounds from all channels, not just the center. It will make noise, but it won't be right (and your receiver will think you have a center channel, so it will send all of the dialogue just to the sub - very bad).

Your best bet is almost certainly to buy a cheap-ish powered subwoofer and use an RCA connection from the receiver to the subwoofer. Passive subs are not very common for the reason you are discovering now. There are certainly external subwoofer amplifiers, but at that point you are putting a bandaid on what was, very likely, not a great subwoofer to begin with.

Thought about the powered sun option because I have one inside that we never use. Only hangup is getting power to the storage chest it would sit in. The speaker wire goes through the wall behind it so I'd have to drill a much bigger hole to get the plug and additional cord through as well. I like the cheap amp option though. I'll look into that. Thanks.

That's what I was thinking about the center channel connection. Might try one of the main channels to see if there is any difference.