Depends whether the staining was actually oil from its coat, which in reality is just going to have attracted soil... your previous cleaning should have dealt with that already.
Might be browning from the fibres being wet, in which case browning prescription or if you want to keep it simple acetic acid may be the answer.
Failing that oxidising might work, I would use something like oxibrite or energiser mixed at 20g per 500ml in a trigger spray, damp towel and iron or use a steamer, but you have to know advanced stain removal techniques before trying this one out, don't try to teach yourself on a custie's carpet!