I would respect your brother’s wishes but if you want to spoil them (and depending on your relationship with him) I would ask/ offer:
1. Any items that he needs them to have and you would actually help by buying (I know I get frustrated when they get mountain of toys but I have to buy the boring stuff they need like clothes). I have often asked uncles to take them
Shopping to buy them certain items and the kids cherish the item and the time they spent with their uncles.

2. Any activity/ time / dinner they would like to do with you

Interestingly my brother did this a few years ago before they had children as they said they weren’t doing presents as they moved house and had had big expenses that year. It subsequently turned out they had given my sisterinlaws family presents but just not ours for whatever reason!
Since then from the following year onwards I’ve suggested we all do secret Santa with a £20-£30 max limit which has to be adhered to and it’s worked really well - no awkwardness and less commercial and more thoughtful all round
All of our children do their own, and us adults do our own
Hope that helps

I also would not do presents.

There will surely be other ways you can treat your niece and nephew - have them to stay and take them out somewhere special for example - then your brother would hopefully not feel obliged to reciprocate in the same way as he might feel with presents. 

Hi

You are coming from a good place and mean well. But your brother has expressed his wish not to do Christmas presents due to financial circumstances.

I think you should respect that and not buy presents. Doing so will likely cause him embarrassment and feelings of shame.

It’s not worth impairing the relationship the two of you have.

It so important for a parent to feel listened to, respected and for the family around them not to overrule their parenting choices. Going against your brother’s wishes is likely to make him hurt, embarrassed and angry . It’s far more important to maintain a great relationship between your and your brothers family than to give a gift.

My brother (probs better off, to be honest) asked to stop doing adult gifts a few years ago, so we just give to the respective kids. If they’re struggling at the mo, and you’re keen to give, could you check with your brother whether it would be ok to give them a (relatively) inexpensive gift like a book, so they know they have been thought of, and then (again if you’re keen and brother agrees) quietly give vouchers directly to your brother towards eg kids’ activities like swimming/an experience for family to do together? Or depending on age of kids - maybe vouchers for shoes - always £££? Have often done that for first birthdays as the grandparents often go crazy on other things anyway.

I think in this instance you should respect your brother's wishes. We stopped this silly merry go round of gift giving to family members years ago and it has been liberating! We just buy gifts for ourselves and our child.

Depending on how well you and your brother get on could you buy something and give it to them from Santa? That would mean you having to get his approval. If he knows that you are better off he may not mind. 

My brother suggested last month that we didn't buy presents this year, he has been quite hard hit for a number of reasons on top of the more widespread ones.

We are more comfortable and I know that my presents are quite spoiling and I don't want my nephew and niece to miss out when things in general their end are quite strained.  I am wanting to find a way to  buy them something anyway without causing embarrassment but not sure how I can do it? Given others may be having similar conversations I thought I would ask.