First, be sure to capture your footage with the standard 29.97fps settings enabled.
Next, you have three options:
#1 - Use After Effects as suggested to convert the frame rate.
#2 - (I recomend this most because it will ensure FCP compatibility) Use the Cinema Tools program to convert the frame rate. It's fast, simple, and instantly agreeable with FCP every time.
Import the movie file that Cinema Tools creates into your FCP bin.
#3 - Work out the difference:
60i is the equivelent of 29.97fps. standard TV at 29.97 captures two fields for every single frame on an odd & even line ratio. 24p captures 23.98 but captures one frame per field. So, all you need to do is work out the ratio difference by dividing to see how many times 29.97 goes into 23.98 (which is about 80% with a small remainder)... then all you really need to do is open up the 60i footage in a sequence set for 29.97fps... change the speed to that ratio of slow motion (about 80%... 80% will work for this just fine as is)... then add a de-interlacing filter to the clip as well.
Export this sequence as a movie.
Now, open a new sequence with a frame rate of 23.98fps, drag & drop your new movie file into this sequence and render it, then export this as yet another movie.
Import that movie file into FCP & you should be set to go.
Anyhow, any of these options should work out for you.
Best of luck!