It's down to what you consider a Communist state, but there are some examples. Most notably, things got a little feisty between the Soviet Union and Maoist China after the Sino-Soviet Split - it even resulted in an undeclared border war in 1969. Then there was the invasion of Cambodia by Vietnam between 1975 and 1977, which ended up toppling the Khmer Rouge. As Vietnam aligned more towards the Soviet Union in hopes of aid against Cambodia, their relations with China soured. This resulted in the short Chinese invasion of Vietnam in 1979, which ended up doing very little.

I guess you could also count the Soviet invasion of Hungary as well. Other than that, you also have some other conflicts which could technically be counted, like the Ogaden War between Ethiopia and Somalia. Both were kinda-I-guess communist states, but when the war broke out the SU chose to back only Ethiopia... which led Somalia to seek out ties with China.

I guess the general trend was that most intra-communist conflicts came from or involved the Sino-Soviet tension.