North1

This.  You aren't likely going to be allowed to let him "live" in the country under a tourist visa.
 
Another suggestion might just be visiting your significant other and waiting out the Canadian immigration.  You'll save yourself a lot of money and frustration in the process.

Unfortunately what you want and what is possible are two different things. 
However I disagree with one poster.  You could certainly have a green card for 2 years and then abandon it.  You can reapply at a later date and while they will ask why, you just tell the truth. 
To be honest the CR1 to citizenship route would be your best bet but will take a minimum of 4-5 years.  It takes about 1 year to get the CR1 visa after marriage.  Your son would need a cr2 visa.  Then it would take 2 years until removal of conditions and at 3 years you can apply for citizenship which also takes about a year to obtain.  At that point you can freely move back and forth and your son would also be a citizen automatically.
 
However there are no visas that allow you to move in with your boyfriend and allow you to work if you do not qualify for a work visa.  

The green card is for permanently residing in the United States (it is conditional for 2 years, not 3).  It's not to be used like a tourist visa back and forth, so you want to be careful with this because you could end up losing legal status in the US if you are found to be spending too much time abroad in Canada.
 
If you do wish to keep legal status while abroad in Canada, you would have to apply for a re-entry permit  before leaving the US which allows an extended period of stay as a green card holder.
 
 

Well you can't work on a k1 visa. So, if you want to work that's not an option. Spousal visas and k1 visas are for people who want to immigrate and live in the United States. Not people who want to temporarily live there and then move back to Canada. 
 
The conditional green card is 2 years not 3 and it takes a while to receive it. If you have your green card and stay out of the country for more than half the year you risk losing your green card as you aren't residing in the United States. 
 
You could come back eventually, but you'd have to reapply again if you were wanting to work. If you don't work as a Canadian you can visit for tourist purposes. 

Does your occupation qualify for  a TN visa?  If so, this might be the way to go right now --- find employment that meets TN requirements and you can work immediately, married or not.

Option 1: K-1 visa.
ETA: ~7-9 months to obtain.
You must marry within 90 days of entry.
You cannot work or travel abroad (and return) until you get an EAD or AP. ETA: ~4 months for those.
Expensive (K-1 costs + AOS costs)
 
Option 2: CR-1 visa. (Must be married already to start the process)
ETA: ~12-14 months to obtain.
You can work and travel abroad (and return).
Cheaper (~$1200) since no AOS is needed.
 
Option 2 looks like the way to go since you stated you need to work. Both options would net you a conditional green card valid for 2 years (not 3 years!), then you need to do ROC. Well, unless you are married for 2+ years at the time you enter on the CR-1 visa or when AOS is approved...but this doesn't sound like it will be the case here.
 
I'm not sure on the requirements to move to Canada, sorry. But if you plan to stay in Canada as your primary residence, then you will need to either abandon the green card (or it will happen automatically) or not bother with getting one in the first case. You cannot live abroad with a green card...it's for permanent residence within the US (not just visits while you live abroad). Being abroad over 12 months sets a presumption of abandoning permanent residence (and just stops by the US to try to "reset" the clock won't work as they look at the totality of the circumstances).
 
If you decide to come back to stay in the US later, you can apply for an IR-1 visa at that time. Visits are still permitted without a green card, though.
 
Another consideration is to get married and do the CR-1 visa route. Then stay in the US for 3 years and apply for citizenship under the 3 year rule (assuming you are still married to the USC at that time). Once you're a USC, you can enter at any time and there's no restriction on how long you can be abroad.