Secure method of encrypting data within a database
Using the same key and IV for different, independently encrypted cells is a bad idea, regardless of which encryption algorithm you use. It would allow attackers to find either XORs of cells (with CTR) or at least equality of prefixes (with CBC).

If you are going to use authenticated encryption, you need to choose whether the MAC applies to each cell independently (which adds data anyway) or the row as a whole.


If you choose the row as a whole, you might want to encrypt the whole row as one, too, since you'll need to read all of it anyway. But if the MAC verification is much faster than decryption, you might still want per-cell encryption with a row-wide MAC.
If you choose per-cell MACs, you are already adding significant data, so you might be able to get away with a per-cell IV too. Or you might be even more determined to avoid adding any extra data, depends on your requirements.


If you end up wanting to do per-cell encryption, but can't have per-cell IVs, CTR is probably your best bet. With CTR the IVs don't need to be random, just unique, so you can calculate the per-cell IV as an offset from the row IV/nonce. Just make sure your offset algorithm will always result in a unique input to each CTR block. E.g. if cells can be at most 256 blocks long, you could use the rightmost byte within the cell, the next one for a cell index and the rest for the row nonce.

CBC is also an option, if you can derive a per-cell IV from the row IV in an unpredictable way. E.g. using $HMAC(k, r || i)$, where $r$ is the row IV and $i$ the row index. That's slower, though. (You could also use the block cipher to derive it.)

Regardless, you should also make sure that the key and IV will differ when a cell is overwritten. With a per-row IV that means the whole row needs to be rewritten with a new IV.

All in all, it's probably simpler to either just have the whole row encrypted and authenticated as a whole or have each cell with their own IV and MAC. Those options allow you to just use an authenticated encryption mode, too.