Please search before you post. Always best to check the obvious. Short Answer. No, Private Races are not available yet. You can however ask your friend to click online and you both click the same race at the same time and you'll both enter the race in MatchMaking Mode.
What me and friends do is use the PS3 clock, since all the clocks are exactly the same time we pick a time say 8:30 and all press start at exactly 8:30 to the second, 99% of the time this works great.
If you pick one of the less popular races at a less popular time (not on the 5 minute mark) there is a fair chance you and your friend will be in there alone.
When you go into the online race menu you can see how many people are racing in any event by the icon to the left. If there is no icon there are very few people racing that event at that time. One head means a few people are racing there. The popular events will have 2 or 3 heads.
If you and your friend are fairly new to GT5P I'd suggest the beginner event at Suzuka East. The Integra is a great car for that track.