Appeal bonds are very, very rare. This is particularly true here where the reason for the jail sentence is failure to show up for probation appointments. But, if your family is going to pay for counsel then that counsel should be moving for the bond anyway. Nothing in the law is impossible. If the bond isn't granted, then there will be little point in an appeal since the appeal process is likely to take at least a year before there is a decision.
Cal. Bar No. 104800
Wis. Bar No. 1020123
He is entitled to a bond during the appellate process because he did not get a sentence of 10 years or more. Whether you want to make that bond is another question. Because he was on probation and revoked, he has the right to appeal the sentence. But, as along as the sentence was within the range of punishment for the offense (which it was), then his chances of succeeding on an appeal are almost none. If the appeal is not successful, he will be required to return to prison (and will not get any credit for time that he is out on an appeal bond.)
In addition to your question about the availability of an appeal bond (which is yes under article 44.04 of the Code of Criminal Proceedure, subject to the approval of the court) you asked about the time fram for an appeal.
The court reporter and clerk would have 60 days from the judgemnt to prepare the record of the trial proceedings. The appellant/defendant would have 30 days to file a brief and the State has another 30 days to respond. Each deadline can be extended on a proper request. Once the briefing is complete, the appellate court would probably issue a ruling within a few months - but that time varies greatly.