Yes, private company can issue convertible debentures. A company issue debentures following procedure will follow:
1. Call a Board Meeting for entering debenture issue agreement. 2. Call an other Board meeting after agreement to call a general meeting for issuing debentures under section 81 (1A) of the Companies Act, 1956. 3. Hold a General meeting and issue a debentures. 4. File a Form-23 with ROC. 5. Hold a Board meeting to allot issued debentures. 6. Issue debentures certificate within 3 months from the date of allotment. 7. Make entry in the register of debentures.
However the provision of section 81(1A) will not apply but you follow the same and must read your company's article to give permission for issue of debentures.