If you're looking for a modern alternative to oils, acrylics give a similar look without the prolonged drying time. It can be hard to tell at a glance whether an artist has used oils or acrylics; I have actually been asked as I'm painting in acrylics whether it's oils I'm using. After all, the only difference between all the painting mediums is the binder holding the pigment together - the pigment (colour) is the same. Acrylics have had a reputation for being garish and, whilst you can have fun and paint some very colourful pictures with them, thay can also be used subtly.
Here's a collection of acrylic portraits to look through, check out the commission process to get an idea of what's involved and feel free to make an enquiry for an acrylic portrait - there's no committment in contacting me and I'd love the opportunity to paint a picture to your desired composition.