Can I build a garage with the 203k program?

Maybe - 
Yes, you can if there is no other garage on the site. If you do have a garage on site, then the new garage may be considered a luxury item and thus not be allowed. 

If you have a home that just needs a garage to be complete, build one with the FHA 203k, no problem.

If you have a two car garage and want to build a new detached garage too, No Can Do.

You can build a detached garage if you want to providing there is no other garage and there is no living area over or attached to that new garage structure.  If there is to be an in-law unit above the garage or in any way attached to that garage, the new garage must share a wall with the existing structure.

In 1994 we were taught that we could attached with breezeway but that is no longer the case. The guideline is being interpreted and misinterpreted to meet the current regime.

Why do I say misinterpreted? Simply because they still think "only 5 draw inspections can be financed into the loan" which other lenders interpret means no more than five draws are allowed. That part of the guideline actually states "On a project of $10,000 no more than five draws are allowed". They all quote the last half of that sentence but clearly by any rational person's interpretation on a project of $250,000 in construction maybe there could be a few more.

Attention Realtors, you have a client and you have found the best house in the world for them but it doesn't have a garage, attached or detached. No problem, it is an FHA 203k loan. Sell them on getting a 203k consultant and having their new loan include the cost of the new garage. Right now that is about  $20-30,000 depending on the size. We just finished a two-car detached garage for $28,000 that was over sized to accommodate a small work shop and another that was $20,000 without a garage door. The borrower wanted to get that outside the 203k. 

This home fit the client's needs in every other way than the garage. A couple acres, but the built-in garages had been coverted with permits and now they just had a carport under the deck. 

Downtown