After playtesting several games I use the following rules for a solitair game (inspired by the iPhone solitair variant):
Goal of the game: To score as many points as possible by completing cities and streets in a small playing area.
You need: Carcassonne base game, counters/chits with numbers 2 to 10 either for streets and cities (or just sheet of paper and a pen).
Extra preparation: Make a pile either of the street and city counters with 10 at the bottom up to 2 at the top. This will show you the size of the next city and street you have to complete. (Write down the numbers 2 up to 10 either for streets and cities.)
Gameplay: Begin with the start-tile. Take further tiles randomly.
The first city and the first street to score must have 2 tiles, the next 3 tiles, 4 tiles and so on. City and street building is independent from each other. There's no need to use meeples to show the ownership. If you complete cities or streets in this order, you score 25 points for every tile of the city or the street. As a reminder lay down the corresponding counter on the last tile. Only one city and street of this size can be scored, but it is possible to score several features with one tile, either street and city, but also two or more cities or streets, if one of them has the appropriate size and the other has one tile more and so on.
If you lay a tile and don't complete any street or city, you have to score negative points: Count the length and width of your playing area and the sum is the amount of points to score negative.
You lost the game, if you laid the last tile and your final score is negative. You win with a positive final score, but try to get an even higher score.
Variant: Shuffle either the street- and city-counters and try to complete features in this random order.
I decided to use the 25 points per tile scoring for two reasons: Scoring of cities streets with size of 2 to 6 tiles score 1000 points exactly like the points you have in the iPhone version. Scoring 25 points means you score 50 points for two tiles, this is one round on the soring board, so it's easy to score.
I use a green meeple to score positive, a red meeple for negative (only one colour is present at one time). For every round on the scoreboard I put a red or green meeple on the zero field. Scoring 50 points for two tiles is to take away one red meeple or to put down another green meeple.
In this version it is possible to score cities or streets sized more than 6 tiles, so it is not really the same as on the iPhone. Besides it is nearly impossible to repeat the same game - but it is possible to play a different game nearly every time.
Accept the challenge and have fun!