If the camera is shooting into the privacy of your house and your activities on your own property, that is referred to as eavesdropping and only law enforcement can obtain a search warrant for such cameras. You can seek an injunction from a civil court requiring them to take down the camera.
The information provided in this answer does not create an attorney-client relationship. If you are interested in his legal services, feel free to call Chris at (303) 409-7635 at his law office in the Denver Tech Center. All initial consultations are free of charge.
Take a look at Schiller v. Mitchell, 357 Ill. App. 3d 435 (Ill. App. Ct. 2d Dist. 2005). The facts of the case are very similar to what you describe. A link to the case opinion is provided below.
You may request an injunction. But if your neighbors are not videorecording your backyard for a government agency or if they can prove they have reasonable justifications for recording your backyard activities, your chances of obtaining the injunction could be low.
A Colorado invasion of privacy lawyer would need to know more facts to tell you if you have a viable invasion of privacy claim. For instance, if the camera is placed somewhere where a person of normal height who was standing in your neighbors' backyard or a public area would not be able to see the same images the camera records, you could have a viable invasion of privacy claim.
Also, if you have persuasive evidence that your neighbors' conduct is racially motivated and calculated to cause you severe emotional distress or drive you out of the neighborhood, you could have other viable claims.
Contact a Colorado invasion of privacy lawyer to learn more about your legal options and the costs associated with pursuing each option.
Please take your photos to an attorney to discuss this. Your attorney may also advise you to contact the police regarding the camera and your neighbor's behavior. However, none of that will make you feel safe if your home. You may contact your city government to ask them if they have any sort of community mediation. Having a neutral party help you meet with your neighbor and talk about their behaviors and your concerns might help alleviate some of their phobias and encourage them to be better neighbors. I'm sorry to hear this is happening to you.
My firm, and many others near you, offer free consultations. Please do consider consulting with an attorney so they can help you determine whether your neighbors have crossed the line.
This legal information is provided for general legal purposes and does not establish a client-attorney relationship. Because of the limited information provided in the question, it is difficult to be certain that Counsel is answering the question correctly. You are encouraged to seek further information from an attorney directly so that follow up questions may be asked if necessary.