Maurice Edu and Kyle Bartley – who have since left the club – were sent the messages by Convery on Twitter after a game against St Johnstone in Perth on 14 January, 2012.
Bartley, 22, said that he found the messages “intimidating” and thought that “society had got over these sorts of comments”.
American Edu, 27, described feeling shocked on seeing the messages he had been sent.
Convery, 43, from Linthouse, Glasgow, had denied sending the messages but was convicted yesterday following a trial at Glasgow Sheriff Court.
Although none of the messages were read out in full in open court, it was heard that Bartley was sent a direct comment from Convery and was mentioned in a second one, and Edu was sent two direct comments.
Bartley told the court he checked his Twitter account after a match with Rangers while travelling home on the team bus and saw tweets from an account in the name of Michael Convery.
He also saw a message had been sent to team mate Edu.
He said: “I was sat next to Maurice on the coach. So we showed each other the comments.”
The player was asked what he did when he received a particular message.
He said: “I actually re-tweeted the tweet. It allowed the public eye to see the comments, and I reported it to David Martin, who is head of security at Glasgow Rangers.”
The court heard that the word “monkey” was used, a comment Bartley said “he was used to”.
Procurator fiscal depute Jonathan Kemp asked how he felt on receiving them and the witness said: “I just felt a little bit hurt and disappointed, really.
“I thought, it’s 2012, I just thought society had got over these sorts of comments.
“Obviously, I don’t know Michael Convery. I didn’t understand why he would have so much hate for me.”
Bartley was asked about another comment which had the words, “You’re a dead coon walking” in it and mentioned his name, but was not sent directly to him.
He said “coon” was a known racist word and was “very insulting”.
The player said he lived on his own and could not always have security with him, adding: “I was intimidated.”
Edu told the court he was shocked and embarrassed when he saw the first message that was sent to him.
The footballer said he looked on the page associated with Convery and there were similar “aggressive” tweets.
He said that, later that day, after receiving another message, he was still shocked and added: “I think that time was when I
The court heard that in his police interview, Convery told officers that on the date of the offence he was suffering from food poisoning and was drifting in and out of consciousness in his house.
He said that his then-16-year-old son was in his house with a friend at the time the tweets were sent. In evidence, Convery told the court he suspected that his teenage son was to blame, although he claimed he did not see any comments being posted.
Convery accepted the Twitter messages came from his BlackBerry phone and his Twitter account.
The court heard evidence that there had been searches using the search engine Google, hours after the tweets were sent, for the subject: “How to delete Twitter.”
Convery was branded an unreliable witness by Sheriff Valerie Johnston before she jailed him.