There are many cheap carbon monoxide detectors available, however there are only a few that I consider good enough to use in your home.
Probably the single biggest problem I see with the less expensive options is that many of them run exclusively on mains power - this is a serious issue because they will fail during a power blackout which is one of the times you are in most need of their protection. This is because many people will naturally use fossil fuel to do things like run a generator, turn on gas powered lamps for lighting, use gas powered cookers designed for camping in the outdoors, or even simply use the fireplace to create some warmth. All of these things can lead to a dangerous build up of carbon monoxide gas.
The only cheap CO Detectors you should use are ones with batteries.
Following are some of the better cheap options which do have battery power and are all sold for less than $25.
First Alert CO400 Carbon Monoxide Detector
First Alert are the other leading manufacturer of CO Detectors and the CO400 is the best of their low-cost options which is powered by a 9v battery which should be replaced every year. Again First Alert have reduced the cost by not providing a digital readout, however you won't miss the 85 decibel alarm when it sounds due to dangerous CO levels in your home. Although this is an acceptable cheap carbon monoxide detector, if you want a digital display then I suggest you get First Alert's higher end CO615 instead which uses both mains and battery power.
The CO400 also has a 5 year warranty and needs to be replaced after this time.
Floureon Battery Powered Carbon Monoxide Alarm
Although Floureon are better known for phone and laptop chargers, this CO Alarm has one substantial benefit over it's better known rivals above in that it has a digital display. At any time you can see what the exact levels of CO gas are in your home, and with the press of a button you can see what the highest level detected was since you last checked. It runs on 3 AAA batteries and although it's cheaper than the ones listed above, the digital display takes its toll on the batteries and you may need to replace them 2 or 3 times a year - it beeps and tells you via the display when the batteries need replacing.
The Floureon has a maximum life of 5 years but does not come with a warranty.
Kidde KN-COB-B-LPM Carbon Monoxide Detector
Kidde are one of the leading manufacturers of CO Alarms and the KN-COB-B-LPM is the cheapest one in their range that I'm able to recommend. When you buy one they come with 3 AAA batteries included - Kidde recommend you replace the batteries at least once a year and the red LED on the front panel with flash once every 60 seconds if the batteries need replacing sooner. Kidde have reduced the cost of this detector by not providing a digital readout - you can't see how much CO gas is present, instead you'll only know if the levels are getting problematic when its alarm sounds. If you want a digital readout then you should get its big brother instead - the KN-COPP-B-LPM.
The KN-COB-B-LPM comes with a 5 year warranty and needs to be replaced after this time.
Although these cheap detectors will save you money in the short term, you may find their constant need for replacement batteries makes them more expensive to own in the long run. If you have a few extra dollars to spare then I recommend you check out my reviews of the best carbon monoxide detectors. In particular you might like to consider the Kidde C3010D which has a built in lithium battery that lasts for the entire life of the detector which is guaranteed for 10 years.