I am currently a tenure track faculty in a college and I plan to look for a position somewhere else. A problem is that, I can not get a teaching letter from my department (in fact I would like to keep my search confidential). Teaching letters are required in my field and I am wondering what should I do in this case? Thank you for your suggestions in advance.
As noted in my response to @strongbad, I recommend against being open about job searches if you're in a T-T position. You don't have to look far to find a lot of horror stories about chairs and senior faculty making life difficult for the 'uppity' young faculty member "who thinks s/he is too good for this school." Best to keep plans close to the chest until you're at a more definitive place in a search.
So that being said...
First, if you have a trusted friend at a nearby college who is in the same or related discipline, you might ask them to do an observation and evaluation of your teaching.
Second, your college's teaching center may be able to do an evaluation but this involves you trusting them not to spill the beans.
Finally, if this is a middle or senior position (i.e. Associate or Full) you can ask in your cover letter that because you the need for discretion because you are already in a tenure-track position, that the request letters be delayed until you make the long short list. This at least buys you time and puts you in a difficult situation only if you're a serious candidate.
I've seen this done and it's not an unusual request. You can suggest that you will provide your full teaching evaluations and portfolio in lieu of a letter until you make the long-short list.
How to get a “teaching letter” when I don't want my department to know I'm looking for a job?
At the risk of stating the obvious: you can't -- at least, not if you want your letter to reflect current information about you, and not if by "my department" you mean "even one person in my department".
More optimistically however, the logic that says that it's highly undesirable to let your current employers know about your job search plans is not entirely watertight, as I explained in a past answer discussing a somewhat similar question. Your department chair would be the most appropriate person to ask for a letter about your teaching. Assuming he/she is a trustworthy, professional and ethical person, you should simply ask them not to disclose your plans to your colleagues within your department. Department chairs quite regularly deal with sensitive information of this sort, and those who are reasonably good at their jobs will have no trouble respecting your wishes.
With that said, I recognize that there are probably some unprofessional department chairs out there who would fail to respect your confidentiality in such a situation, or may even be tempted to sabotage your plans by writing a dishonest letter. If you are worried about not being treated fairly by your chair, I would suggest finding some other colleague within the department to ask for the letter from. The bottom line is you would need to be able to identify at least one person who is qualified to evaluate your teaching performance in your current job and whom you can trust to keep your plans confidential and not to act vindictively against you because of the slight conflict of interest inherent in your situation. If you can't find such a person, I'm not really sure what else to suggest. Good luck!
You say you cannot get a teaching letter from your department. Presumably this is because you want to keep the search confidential. You should consider if it really matters if colleagues find out. The only case I think it is a big deal is if you are trying to escape a toxic environment and taking a step down. Most reasonable colleagues will understand if you are trying to get a promotion, raise, better school, or better location.