i can't come: gelemiyorum, gelemem

gelebiliyorum is not mostly used type. very rare used. and it expresses an approval after one's have been asked. for example: i asked you to join my party next week, if you have free time and nothing planned. and you replied me "ok, let me think some, later i will inform you". then, afew days later you called me and told "well, i evaluated my next week and i decided to come, so gelebiliyorum". what about gelebilirim? it is same but said just after you have been asked. i ask you now and you answer me now. secondly, it is an answer to such type of questions: can you come........? yes i can come (gelebilirim)

Tenses are different but they mean the same thing. If you search "Positive Potential Mood" examples online you can easily see the explanations about it. Potential Mood -Present Continuous Tense: gelebiliyorum - I can come, I am able to come, I may come, I might come Potential Mood - Present Simple Tense: gelebilirim - I can come, I am able to come, I may come, I might come Plus to answer your question about how to say "I can't come" ~ Gelemem.